Algebra I B
The function f(x) = is reflected across the y-axis to create the function g(x). Which ordered pair is on g(x)?
A
Which is the graph of f(x) = (4)x?
D
What is the initial value of the exponential function shown on the graph? 0 1 2 4
D
Ms. Johnson uses a statistics program to analyze all the data collected by her students during a lab experiment about acceleration due to gravity. The program reports =31.5 and . What is the variance of the data? Round to the nearest tenth. 1.6 2.5 5.6 6.3
6.3
What is the additive inverse of the polynomial -9xy2 + 6x2y - 5x3? -9xy2 - 6x2y + 5x3 -9xy2 - 6x2y - 5x3 9xy2 + 6x2y + 5x3 9xy2 - 6x2y + 5x3
D
Which table shows exponential decay?
A
Which is a stretch of an exponential decay function? f(x) = f(x) = f(x) = f(x) =
C
The table represents an exponential function. What is the multiplicative rate of change of the function? 1/3 2/3 2 9
2/3
What is the simplified value of the exponential expression ? 3 9
3
The graph represents the distribution of the number of questions answered correctly on a 50-question math test. What is the standard deviation of the data? 4 8 12 24
4
The graph shows the distribution of hand lengths, in centimeters, of the members of an orchestra. What is the variance of the data? 1 2 4 5
4
A growth medium is inoculated with 1,000 bacteria, which grow at a rate of 15% each day. What is the population of the culture 6 days after inoculation? y = 1,000(1.15)6; 2,313 bacteria y = 1,000(1.15)7; 2,660 bacteria y = 1,000(1.5)5; 7,594 bacteria y = 1,000(1.5)6; 11,391 bacteria
y = 1,000(1.15)6; 2,313 bacteria
The factor tree for 1,764 is shown. What is the simplest form of ? 21 42 32(72) 22(32)(72)
42
What is the vertex of the graph of f(x) = |x + 3| + 7? (3, 7) (7, 3) (-3, 7) (7, -3)
(-3, 7)
The piecewise function h(x) is shown on the graph. What is the value of h(2)? −2 −1 0 3
0
Which value for R in the table would most likely indicate an association between the conditional variables? 0.09 0.10 0.13 0.79
0.79
Which is the initial value that shrinks an exponential growth function by 50%?
1/2
A relative frequency table is made from data in a frequency table. What is the value of g in the relative frequency table? Round the answer to the nearest percent. 25% 33% 63% 68%
33%
A piecewise function is defined as shown. What is the value of f(x) when x=3? −3 −2 1 4
4
Which is equivalent to ? 4 12 64 192
64
Unit Test
88%
Which graph represents a reflection of f(x) = 2(0.4)x across the y-axis?
A
Which term could be put in the blank to create a fully simplified polynomial written in standard form? 8x3y2−_____+3xy2−4y3 x2y2 x3y3 7xy2 7x0y3
A
Use the graphing calculator to graph the function f(x) = . Which table of values contains points that lie on the graph of the function?
C
What is the initial value of the exponential function shown on the graph? 0 1 2 4
C
Which graph represents the function p(x) = |x - 1|?
D
Which statement is true about the function f(x)= -? The domain of the function is all negative real numbers. The range of the function is all positive real numbers. The domain and range of the function have opposite signs. The domain and range of the function are the same.
The domain and range of the function are the same.
The graph of f(x) = (2.5)x and its reflection across the x-axis, g(x), are shown. What is the range of g(x)? all real numbers all real numbers less than 0 all real numbers greater than 0 all real numbers less than or equal to 0
all real numbers less than 0
Which equation represents an exponential function that passes through the point (2, 80)? f(x) = 4(x)5 f(x) = 5(x)4 f(x) = 4(5)x f(x) = 5(4)x
f(x) = 5(4)x
The function g(x) is defined as shown. What is the value of g(0)? −2 −1 3 6
−1
Which graph is the result of reflecting f(x) = (8)x across the y-axis and then across the x-axis?
D
Which is equivalent to ?
D
Which is equivalent to ? 3 6 36 72
D
Which is the graph of ?
D
What is the rate of increase for the function f(x) = ? 2 4 4
D 4∛9
What are the domain, range, and asymptote of h(x) = 2x + 4? domain: {x | x > 0}; range: {y | y is a real number}; asymptote: y = 0 domain: {x | x > -4}; range: {y | y is a real number}; asymptote: y = -4 domain: {x | x is a real number}; range: {y | y > 0}; asymptote: y = 0 domain: {x | x is a real number}; range: {y | y > 0}; asymptote: y = -4
domain: {x | x is a real number}; range: {y | y > 0}; asymptote: y = 0
Ginny is studying a population of frogs. She determines that the population is decreasing at an average rate of 3% per year. When she began her study, the frog population was estimated at 1,200. Which function represents the frog population after x years? f(x) = 1,200(1.03)^x f(x) = 1,200(0.03)^x f(x) = 1,200(0.97)^x f(x) = 1,200(0.97)x
f(x) = 1,200(0.97)^x
Terrence buys a new car for $20,000. The value of the car depreciates by 15% each year. If f(x) represents the value of the car after x years, which function represents the car's value? f(x) = 20,000(0.85)x f(x) = 20,000(0.15)x f(x) = 20,000(1.15)x f(x) = 20,000(1.85)x
f(x) = 20,000(0.85)x
Hal is asked to write an exponential function to represent the value of a $10,000 investment decreasing at 2% annually. What multiplicative rate of change should Hal use in his function? 0.02 0.98 1.02 1.98
0.98
Absolute Value Functions and Translations
100%
Nonlinear Functions Linear Piecewise Defined Functions
100%
A gym offers three levels of membership based on the number of visits per month, as represented by the table. Kaleigh wants to know how much she will pay for her gym membership. Which graph represents the total monthly cost at the gym as a function of the number of visits Kaleigh plans to make each month?
A
What is the rate of change of the function described in the table? 5 25
B
Which equation represents the function graphed on the coordinate plane? g(x) = |x - 4| - 10 g(x) = |x + 4| - 10 g(x) = |x - 10| + 4 g(x) = |x + 10| - 4
g(x) = |x + 4| - 10
Ramon is graphing the function f(x) = 3(4)x. He begins by plotting the initial value. Which graph represents his initial step?
A
The function D(t) defines a traveler's distance from home, in miles, as a function of time, in hours. Which times and distances are represented by the function? Select three options. The starting distance, at 0 hours, is 300 miles. At 2 hours, the traveler is 725 miles from home. At 2.5 hours, the traveler is still moving farther from home. At 3 hours, the distance is constant, at 875 miles. The total distance from home after 6 hours is 1,062.5 miles.
At 2 hours, the traveler is 725 miles from home. At 3 hours, the distance is constant, at 875 miles. The total distance from home after 6 hours is 1,062.5 miles.
The graph of y = is reflected over the y-axis and then translated down 2 units to form f(x). Which is the graph of f(x)?
B
Which graph shows exponential growth?
B
On each coordinate plane, the parent function f(x) = |x| is represented by a dashed line and a translation is represented by a solid line. Which graph represents the translation g(x) = |x + 2| as a solid line?
C
Profit is the difference between revenue and cost. The revenue, in dollars, of a company that manufactures cell phones can be modeled by the polynomial 2x2 + 55x + 10. The cost, in dollars, of producing the cell phones can be modeled by 2x2 - 15x - 40. The variable x represents the number of cell phones sold. What expression represents the profit, and what is the profit if 240 cell phones are sold? 40x - 30; $2,400 40x - 30; $9,570 70x + 50; $16, 850 70x + 50; $28,800
C
The data set represents the total number of people who bought bananas each hour at a grocery store. 1, 1, 5, 5, 7, 8, 8, 10, 12 Which box plot correctly represents the data?
C
Which expression is equivalent to ?
C
Which is true about the degree of the sum and difference of the polynomials 3x5y - 2x3y4 - 7xy3 and -8x5y + 2x3y4 + xy3? Both the sum and difference have a degree of 6. Both the sum and difference have a degree of 7. The sum has a degree of 6, but the difference has a degree of 7. The sum has a degree of 7, but the difference has a degree of 6.
C
Which table represents points on the graph of h(x) = ?
C x -6 1 2 3 -10y 2 1 0 -1 -2
The graph of g(x) is a reflection and translation of f(x)=3/x. Which equation represents g(x)? g(x) = g(x) = g(x) = g(x) =
D
Which algebraic expression is a polynomial? 3m2n - + - + 4m5 - 3mn5 + 7mn + +
D
Which best describes the range of the function f(x) = 2/3 (6)x after it has been reflected over the x-axis? all real numbers all real numbers less than 0 all real numbers greater than 0 all real numbers less than or equal to 0
D
Which cube root function is always decreasing as x increases? f(x) = f(x) = f(x) = f(x) =
D
Which equation represents an exponential function that passes through the point (2, 36)? f(x) = 4(3)x f(x) = 4(x)3 f(x) = 6(3)x f(x) = 6(x)3
f(x) = 4(3)x
Josiah invests $360 into an account that accrues 3% interest annually. Assuming no deposits or withdrawals are made, which equation represents the amount of money in Josiah's account, y, after x years? y = 360(1.3)x y = 360(0.3)x y = 360(0.03)x y = 360(1.03)x
y = 360(1.03)x
What is the domain of f(x) = 5x - 7? {x | x > -7} {x | x < -7} {x | x > 0} {x | x is a real number}
{x | x is a real number}
Use the graphing calculator to graph the function f(x) = -. Which list contains three points that lie on the graph of the function? (-9, 3), (-4, 2), (-1,1) (1,1), (4, 2), (9, 3) (-9, -3), (-4, -2), (-1,-1) (1,-1), (4, -2), (9, -3)
(1,-1), (4, -2), (9, -3)
The piecewise function h(x) is shown on the graph. What is the value of h(3)? -2 -1 1 2
1
The Cube Root Function
100%
The Square Root Function
100%
What is the simplified form of /144x36? 12x6 12x18 72x6 72x18
12x18
The solid graph is a translation of . How was the graph of shifted to form the translation? 2 units up 2 units down 2 units left 2 units right
2 units up
Which graph represents the function f(x) = |x + 3|?
B
The graph shows the function g(x) for a restricted domain. Which is the function g(x) for a restricted domain? g(x) = ; x -4 g(x) = ; x 0 g(x) = ; x -4 g(x) = ; x 0
g(x) = ; x -4
The graph shows the function f(x) = |x - h| + k. What is the value of k? k = -2.5 k = -1 k = 1 k = 2.5
k = -2.5
A piecewise function is represented by the graph below. What is the domain for the piece of the function represented by f(x) = x + 1? x < -1 -1 ≤ x ≤ 1 1 ≤ x < 2 x > 1
x > 1
Over which interval is the graph of the parent absolute value function decreasing? (-∞, ∞) (-∞, 0) (-6, 0) (0, ∞)
(-∞, 0)
Which could be the graph of f(x) = |x - h| + k if h and k are both positive?
A
The table represents an exponential function. What is the multiplicative rate of change of the function? 0.2 0.25 0.5 0.75
0.5
Translations of Exponential Functions
100%
Unit Test Review
100%
What is the simplified form of 100x36? 10x18 10x6 50x18 50x6
10x18
Which could be a conditional relative frequency table?
B
Which table represents exponential growth?
B
Which is an exponential decay function?
C
Exponential Decay Functions
100%
The two-way frequency table represents data from a survey asking mall visitors whether they like seafood, meat, or both. Which is the joint relative frequency for mall visitors who like seafood and meat?
16/72
The graph shows that is translated horizontally and vertically to create the function . What is the value of h? −2 −1 1 2
2
What is the simplified value of the exponential expression ? 2 4
2
The function g(x) is defined as shown. What is the value of g(3)? 2 3 9 14
3
On each coordinate plane, the parent function f(x) = |x| is represented by a dashed line and a translation is represented by a solid line. Which graph represents the translation g(x) = |x| - 4 as a solid line?
A
The curve through the ordered pairs (0, 10), (1, 5), and (2, 2.5) can be represented by the function f(x) = 10(0.5)x. What is the multiplicative rate of change of the function? 0.5 2 2.5 5
A
The graph of the cube root parent function y = is translated to form f(x) shown on the graph. Which equation represents f(x)? f(x) = f(x) = f(x) = f(x) =
A
The table represents an exponential function. What is the multiplicative rate of change of the function? 1/5 2/5 2 5
A
What is the difference of the polynomials? (-2x3y2 + 4x2y3 - 3xy4) - (6x4y - 5x2y3 - y5) -6x4y - 2x3y2 + 9x2y3 - 3xy4 + y5 -6x4y - 2x3y2 - x2y3 - 3xy4 - y5 -6x4y + 3x3y2 + 4x2y3 - 3xy4 + y5 -6x4y - 7x3y2 + 4x2y3 - 3xy4 - y5
A
What is the difference of the two polynomials? (9x2 + 8x) - (2x2 + 3x) 7x2 + 5x 7x2 + 11x 11x2 + 5x 11x2 + 11x
A
What is the range of f(x) = - 4? {y | y > -4} {y | y < -4}
A
Which is the graph of f(x) = 5(2)x?
A
Which is the graph of g(x) = 2x - 1 + 3?
A
Which polynomial is represented by the algebra tiles? 2x2 - 4x - 6 2x2 + 4x + 6 -2x2 - 4x - 6 -2x2 + 4x + 6
A
Which terms could be used as the first term of the expression below to create a polynomial written in standard form? Select five options. + 8r2s4 - 3r3s3 s5 3r4s5 -r4s6 -6rs5
A, B, C, D, E
Which could be the missing first term of the expression that, when fully simplified, would be a binomial with a degree of 4? Select three options. ________ - 5xy3 + 9x2y 0 5xy3 9x2y 8y4 4xy3
A,C,E
For the polynomial 6xy2−5x2y?+9x2 to be a trinomial with a degree of 3 after it has been fully simplified, what is the missing exponent of the y in the second term? 0 1 2 3
B
Kat is painting the edge of a triangular stage prop with reflective orange paint. The lengths of the edges of the triangle are (3x - 4) feet, (x2 - 1) feet, and (2x2 - 15) feet. What is the perimeter of the triangle if x = 4? 16 feet 40 feet 76 feet 80 feet
B
The function f(x) = 2·5x can be used to represent the curve through the points (1, 10), (2, 50), and (3, 250). What is the multiplicative rate of change of the function? 2 5 10 32
B
The function g(x)=8(4x) is reflected across the x-axis to create f(x). What is the equation of f(x)? f(x)=8(4)x f(x)=−8(4)x f(x)=8 f(x)=−8
B
The factor tree for 3,025 is shown. What is the simplest form of ? 16 55 52(112) 52+(112)
C
The function f(x) is defined as f(x) = (6)x. Which table of values could be used to graph g(x), a reflection of f(x) across the x-axis?
C
The piecewise function f(x) has opposite expressions. f(x) = Which is the graph of f(x)?
C
Which equation represents an exponential function with an initial value of 500? f(x) = 100(5)x f(x) = 100(x)5 f(x) = 500(2)x f(x) = 500(x)2
C
Which function represents g(x), a reflection of f(x) = 4 across the x-axis? g(x) = −4(2)x g(x) = 4(2)−x g(x) = −4 g(x) = 4
C
Which set of steps will translate f(x) = 6x to g(x) = 6x - 5 - 7? Shift f(x) = 6x five units to the left and seven units up. Shift f(x) = 6x five units to the right and seven units down. Shift f(x) = 6x seven units to the right and five units up. Shift f(x) = 6x seven units to the left and five units down.
Shift f(x) = 6x five units to the right and seven units down.
The dot plot shows the number of words students spelled correctly on a pre-test. Which statement best describes the shape of the graph? The graph is skewed right. The graph is nearly symmetrical. The graph is skewed left. The graph is perfectly symmetrical.
The graph is nearly symmetrical.
Which equation represents the function f(x) = (1.6)x after it has been translated 5 units up and 9 units to the right? g(x) = (1.6)x + 5 − 9 g(x) = (1.6)x + 5 + 9 g(x) = (1.6)x − 9 + 5 g(x) = (1.6)x + 9 + 5
g(x) = (1.6)x − 9 + 5
Which equation represents the function graphed on the coordinate plane? g(x) = |x + 4| - 2 g(x) = |x - 4| - 2 g(x) = |x - 2| - 4 g(x) = |x - 2| + 4
g(x) = |x + 4| - 2
A limited-edition poster increases in value each year with an initial value of $18. After 1 year and an increase of 15% per year, the poster is worth $20.70. Which equation can be used to find the value, y, after x years? (Round money values to the nearest penny.) y = 18(1.15)x y = 18(0.15)x y = 20.7(1.15)x y = 20.7(0.15)x
y = 18(1.15)x
The graph of the piecewise function f(x) is shown. What is the domain of f(x)? {x | 1 < x < 5} {x | 1 < x < 5} {y | −4 < y < 1} {y | −4 < y < 1}
{x | 1 < x < 5}
Tanisha is graphing the function f(x) = 25()x. She begins by plotting the point (1, 15). Which could be the next point she plots on the graph? (2, 9) (2, -10) (2, 14) (2, 5)
(2, 9)
The data set represents the total number of tickets each person purchased for a play. 0, 0, 1, 1, 1, 2, 2, 2, 4, 4 What is the median of the data? 1 1.5 2 2.5
1.5
Blanca runs 8 laps around the track each day to train for an endurance race. She times each lap to practice her pacing for the race. The table shows the lap times, in seconds, for three days of practice. Which histogram represents Blanca's lap times for the three days of practice?
A
The graph of g(x) is the result of translating the graph of f(x) = 3x six units to the right. What is the equation of g(x)? g(x) = 3x - 6 g(x) = 3x + 6 g(x) = 3x - 6 g(x) = 3x + 6
A
The sum of two polynomials is 8d5 - 3c3d2 + 5c2d3 - 4cd4 + 9. If one addend is 2d5 - c3d2 + 8cd4 + 1, what is the other addend? 6d5 - 2c3d2 + 5c2d3 - 12cd4 + 8 6d5 - 4c3d2 + 3c2d3 - 4cd4 + 8 6d5 - 4c3d2 + 5c2d3 - 12cd4 + 8 6d5 - 2c3d2 - 3c2d3 - 4cd4 + 8
A
Which is the graph of f(x) = 2(3)x?
A
Kira looked through online census information to determine the average number of people living in the homes in her city. What is true about Kira's data collection? Kira used an observational study where the data is qualitative. Kira used an observational study where the data is quantitative. Kira used published data that is qualitative. Kira used published data that is quantitative.
Kira used published data that is quantitative.
The box plots compare the exam scores of Ms. Dobson's class to the rest of the students who took the test in the district. Which statement is true about the box plots? Select three options. Ms. Dobson's class has a smaller range of scores. The district has a greater interquartile range. Fifteen is an outlier for the district's scores. One hundred is an outlier for the district's scores. In general, the district's scores were better than those of Ms. Dobson's class.
Ms. Dobson's class has a smaller range of scores. The district has a greater interquartile range. Fifteen is an outlier for the district's scores.
The graph of g(x) is shown. Which statements describe the domain and range of g(x)? Select two options. The function g(x) is defined for all real numbers x. The maximum value of the range is 4. The maximum value of the domain is 3. The range of g(x) is {y| -1 < y ≤ 4}. The domain of g(x) is {x| -4 < x ≤ 3}.
The maximum value of the range is 4. The range of g(x) is {y| -1 < y ≤ 4}.
Violet creates two spinners for a game. Each spinner is spun once, and the sum is recorded. The table represents the sums of the spinners and the frequency of each sum. What statement is true about the mean of the sums of the two spinners? The mean is 12. The mean is 16. The mean is the same as the median. The mean is the same as the range.
The mean is the same as the median.
The function f(x) = is shown on the graph. Which statement is correct? The domain of the function is all real numbers less than or equal to −1. The range of the function is all real numbers greater than or equal to 0. The range of the function is all real numbers less than or equal to 0. The domain of the function is all real numbers less than or equal to 0.
The range of the function is all real numbers less than or equal to 0.
Ms. Sutton recorded the word counts and scores of the top ten essays in a timed writing contest. The table shows her data. How does the word count of an essay relate to its score in the contest? Word count tends to decrease as the score decreases. Word count tends to increase as the score decreases. Word count tends to remain constant as the score decreases. Word count has no apparent relationship to the score of the essay.
Word count has no apparent relationship to the score of the essay.
A group of campers were polled about whether they like swimming and whether they like playing baseball. The data from the survey is shown in the Venn diagram. Use the Venn diagram to find the missing values in the frequency table. Which values are correct? Select three options. a = 15 b = 18 c = 23 d = 35 e = 31
a = 15 b = 18 e = 31
What are the domain and range of f(x) = + 2? domain: ; range: {y | y > 0} domain: ; range: {y | y > 2} domain: {x | x is a real number}; range: {y | y > 2} domain: {x | x is a real number}; range: {y | y > -2}
domain: {x | x is a real number}; range: {y | y > 2}
A population of bacteria is treated with an antibiotic. It is estimated that 5,000 live bacteria existed in the sample before treatment. After each day of treatment, 40% of the sample remains alive. Which best describes the graph of the function that represents the number of live bacteria after x days of treatment? f(x) = 5000(0.4)x, with a horizontal asymptote of y = 0 f(x) = 5000(0.6)x, with a vertical asymptote of x = 0 f(x) = 5000(1.4)x, with a horizontal asymptote of y = 0 f(x) = 5000(1.6)x, with a vertical asymptote of x = 0
f(x) = 5000(0.4)x, with a horizontal asymptote of y = 0
Which function has a simplified base of 4? f(x) = 2 f(x) = 2 f(x) = 4 f(x) = 4
f(x)=4(∛64)^2x
The graphs of f(x) = 5x and its translation, g(x), are shown on the graph. What is the equation of g(x)? g(x) = 5x - 9 g(x) = 5x - 10 g(x) = 5x - 9 g(x) = 5x - 10
g(x) = 5x - 10
How are the two functions f(x) = 0.7(6)x and g(x) = 0.7(6)-x related to each other? g(x) is the reflection of f(x) over the x-axis. g(x) is the reflection of f(x) over the y-axis. g(x) is the reflection of f(x) over both axes. g(x) and f(x) will appear to be the same function.
g(x) is the reflection of f(x) over the y-axis.
The graph shows the relationship between daily caffeine consumption and resting heart rate for some adults. Which phrases describe the relationship between heart rate and daily intake of caffeine? Select two options. negative correlation increasing heart rate constant correlation positive correlation decreasing heart rate
increasing heart rate positive correlation
A function, h(x), is defined as shown. h(x) = Which graph represents h(x)?
B
The graph of a function is shown. Which function is represented by the graph? f(x) = f(x) = f(x) = f(x) =
B
The value of a collector's item is expected to increase exponentially each year. The item is purchased for $500 and its value increases at a rate of 5% per year. Find the value of the item after 4 years. $578.81 $607.75 $1687.50 $2531.25
$607.75
What is the simplified form of /64x16? 8x4 8x8 32x4 32x8
8x8
Which graph represents the function f(x) = |x| - 4?
C
Which graph represents the function h(x) = |x| + 0.5?
C
Which describes how to graph by transforming the parent function? Reflect the parent function over the y-axis, and translate it 3 units to the right. Reflect the parent function over the y-axis, and translate it 3 units to the left. Reflect the parent function over the x-axis, and translate it 8 units to the right. Reflect the parent function over the x-axis, and translate it 8 units to the left.
Reflect the parent function over the x-axis, and translate it 8 units to the left.
The function f(x)= is shown on the graph. Which statement is correct? The range of the graph is all real numbers less than or equal to 0. The domain of the graph is all real numbers less than or equal to 0. The domain and range of the graph are the same. The range of the graph is all real numbers.
The domain of the graph is all real numbers less than or equal to 0.
The graph shows the function f(x) = |x - h| + k. What is the value of h? h = -3.5 h = -1.5 h = 1.5 h = 3.5
h = -1.5
The function s(V) = describes the side length, in units, of a cube with a volume of V cubic units. Jason wants to build a cube with a minimum of 64 cubic centimeters. What is a reasonable range for s, the side length, in centimeters, of Jason's cube? s > 0 s > 4 s > 8 s > 16
s > 4
Brenton's weekly pay, P(h) , in dollars, is a function of the number of hours he works, h. He gets paid $20 per hour for the first 40 hours he works in a week. For any hours above that, he is paid overtime at $30 per hour. He is not permitted to work more than 60 hours in a week. Which set describes the domain of P(h)? {h| 0 ≤ h ≤ 40} {h| 0 ≤ h ≤ 60} {P(h)| 0 ≤ P(h) ≤ 1,400} {P(h)| 0 ≤ P(h) ≤ 1,800}
{h| 0 ≤ h ≤ 60}
What is the simplified form of ? Assume x ≠ 0. 6/5x10 6/5x2 6/5 x10 6/5 x2
6/5x10
What is the simplified form of 216x8/60x2? Assume x ≠ 0. 36x3 36x2 6x3 6x2
6x3
The graph of g(x) is a translation of y = . Which equation represents g(x)? g(x) = g(x) = g(x) = g(x) =
A
The graph of g(x) is a translation of y = 3/x. Which equation represents g(x)? g(x) = g(x) = g(x) = g(x) =
A
Which graph represents the function r(x) = |x - 2| - 1
A
Which is the graph of the function f(x) =
A
Which statement is true of the function f(x) = ? Select three options. The function is always increasing. The function has a domain of all real numbers. The function has a range of {y|- < y < }. The function is a reflection of y = . The function passes through the point (3, -27).
B C D
The function f(x) = is shown on the graph. Which statement is correct? The domain of the function is all real numbers greater than or equal to 0. The range of the function is all real numbers greater than or equal to −1. The range of the function is all real numbers less than or equal to 0. The domain of the function is all real numbers less than or equal to 0.
The domain of the function is all real numbers less than or equal to 0.
Which statement is true about the function f(x)= ? The domain of the graph is all real numbers. The range of the graph is all real numbers. The domain of the graph is all real numbers less than or equal to 0. The range of the graph is all real numbers less than or equal to 0.
The domain of the graph is all real numbers less than or equal to 0.
The graph represents the cost of catering a dinner as a function of the number of guests. What is the catering cost for a dinner with 40 guests? $400 $600 $700 $800
$600
The graph of is shown. On which interval is this graph increasing? (-∞, 6) (-∞, 10) (6, ∞) (10, ∞)
(10, ∞)
What is the vertex of the graph of g(x) = |x - 8| + 6? (6, 8) (8, 6) (6, -8) (-8, 6)
(8, 6)
The frequency table shows the results of a survey comparing the number of beach towels sold for full price and at a discount during each of the three summer months. The store owner converts the frequency table to a conditional relative frequency table by row. Which value should he use for X? Round to the nearest hundredth. 0.89 0.90 0.92 0.96
0.90
A store manager is looking at past jewelry sales to determine what sizes of rings to keep in stock. The list shows the ring sizes purchased by the last ten jewelry customers. 9, 7, 6.5, 7.5, 7, 8, 5, 6, 7.5, 8 What is the variance of the data set? Round to the nearest hundredths. 0.40 0.72 1.15 2.14
1.15
Which represents the reflection of f(x) = over the x-axis?
A
Which represents the reflection of f(x) = over the y-axis?
A
Which statements accurately describe the function f(x) = 3? Select three options. The initial value is 3. The domain is x > 0. The range is y >0. The simplified base is 12. The simplified base is 8.
A, C, E The initial value is 3. The range is y >0. The simplified base is 8.
The function s(V) = describes the side length, in units, of a cube with a volume of V cubic units. Jason wants to build a cube with a minimum of 64 cubic centimeters. What is a reasonable range for s, the side length, in centimeters, of Jason's cube? s > 0 s 4 s 8 s 16
B
The graph of f(x) = 2x is shown on the grid. The graph of g(x) = ()x is the graph of f(x) = 2x reflected over the y-axis. Which graph represents g(x)?
B
The graph of g(x) is the result of translating the graph of f(x) = three units to the left. What is the equation of g(x)? g(x) = g(x) = g(x) = g(x) =
B
The graph of h(x) is a translation of . Which equation represents h(x)?
B
The graph shows that f(x)= is translated horizontally and vertically to get the function . What is the value of k? −5 −3 3 5
B
What is the sum of the polynomials? (-x2 + 9) + (-3x2 - 11x + 4) -4x2 - 2x + 4 -4x2 - 11x + 13 2x2 + 20x + 4 2x2 + 11x + 5
B
What is true about the sum of the two polynomials? 6s2t - 2st2 4s2t - 3st2 The sum is a binomial with a degree of 2. The sum is a binomial with a degree of 3. The sum is a trinomial with a degree of 2. The sum is a trinomial with a degree of 3.
B
Which algebraic expression is a polynomial? 4x2 - 3x + -6x3 + x2 - 8x2 + -2x4 +
B
Which equation represents the function graphed on the coordinate plane? g(x) = |x + 1| + 3 g(x) = |x + 3| - 1 g(x) = |x - 1| + 3 g(x) = |x + 3| + 1
B
Which exponential function is represented by the graph? f(x) = 2 f(x) = (2)x f(x) = f(x) = 2(2)x
B
Which function represents a reflection of f(x) = 5(0.8)x across the x-axis? g(x) = 5(0.8)-x g(x) = -5(0.8)x g(x) = (0.8)x g(x) = 5(-0.8)x
B
Which graph represents a reflection of f(x) = (10)x across the y-axis?
B
Which is equivalent to ? 243x
B
Which is equivalent to ? 92x
B
Which is the graph of ?
B
Which is true about the completely simplified difference of the polynomials a3b + 9a2b2 − 4ab5 and a3b − 3a2b2 + ab5? The difference is a binomial with a degree of 5. The difference is a binomial with a degree of 6. The difference is a trinomial with a degree of 5. The difference is a trinomial with a degree of 6.
B
Which is true about the polynomial -8m3 + 11m? It is a binomial with a degree of 2. It is a binomial with a degree of 3. It is a trinomial with a degree of 2. It is a trinomial with a degree of 3.
B
Which statement is true about the polynomial5s6t2 + 6st9 - 8s6t2 - 6t7 after it has been fully simplified? It has 3 terms and a degree of 9. It has 3 terms and a degree of 10. It has 4 terms and a degree of 9. It has 4 terms and a degree of 10.
B
Vertical Stretches and Shrinks of Exponential Functions
C
What is the initial value of the exponential function represented by the table?
C
When simplified, the expression is 12. Which is a possible value of x? 6 24 144 256
C
What are the domain and range of the function on the graph? The domain includes all integers, and the range is y ≥ 0. The domain includes all integers, and the range is y > 0. The domain includes all real numbers, and the range is y ≥ 0. The domain includes all real numbers, and the range is y > 0.
The domain includes all real numbers, and the range is y > 0.
Which are true of the function f(x) = 49? Select three options. The domain is the set of all real numbers. The range is the set of all real numbers. The domain is x > 0. The range is y > 0. As x increases by 1, each y-value is one-seventh of the previous y-value.
The domain is the set of all real numbers. The range is y > 0. As x increases by 1, each y-value is one-seventh of the previous y-value.
Several ordered pairs from a continuous exponential function are shown in the table. What are the domain and range of the function? The domain is the set of integers, and the range is y > 4. The domain is the set of integers, and the range is y > 0. The domain is the set of real numbers, and the range is y > 0. The domain is the set of real numbers, and the range is y > 4.
The domain is the set of real numbers, and the range is y > 0.
Two exponential functions are shown in the table. Which conclusion about f(x) and g(x) can be drawn from the table? The functions f(x) and g(x) are reflections over the x-axis. The functions f(x) and g(x) are reflections over the y-axis. The function f(x) is a decreasing function, and g(x) is an increasing function. The function f(x) has a greater initial value than g(x).
The functions f(x) and g(x) are reflections over the y-axis.
Which best describes the graph of the function f(x) = 4(1.5)x? The graph passes through the point (0, 4), and for each increase of 1 in the x-values, the y-values increase by 1.5. The graph passes through the point (0, 4), and for each increase of 1 in the x-values, the y-values increase by a factor of 1.5. The graph passes through the point (0, 1.5), and for each increase of 1 in the x-values, the y-values increase by 4. The graph passes through the point (0, 1.5), and for each increase of 1 in the x-values, the y-values increase by a factor of 4.
The graph passes through the point (0, 4), and for each increase of 1 in the x-values, the y-values increase by a factor of 1.5.
An exponential function f(x) is reflected across the x-axis to create the function g(x). Which is a true statement regarding f(x) and g(x)? The two functions have the same initial value. The two functions will cross each other on the axis. The two functions have reciprocal output values of each other for any given input value. The two functions have opposite output values of each other for any given input value.
The two functions have opposite output values of each other for any given input value.
A piecewise function g(x) is represented by the graph. Which functions represent a piece of the function? Select three options. g(x) = −2x, −2 < x < 0 g(x) = −2, x < −2 g(x) = x − 2, −2 < x < 1 g(x) = −2x + 6, x ≥ 1 g(x) = + 1, -2 ≤ x < 1
g(x) = −2, x < −2 g(x) = −2x + 6, x ≥ 1 g(x) = + 1, -2 ≤ x < 1
The graph of g(x) = |x - h| + k is shown on the coordinate grid. What must be true about the signs of h and k? Both h and k must be positive. Both h and k must be negative. h must be positive and k must be negative. h must be negative and k must be positive.
h must be negative and k must be positive.
The graph of h(x) is a translation of . Which equation represents h(x)?h(x)=\root(3)(x-2) h(x)=\root(3)(x+2) h(x)=\root(3)(x)-2 h(x)=\root(3)(x)+2
h(x)=\root(3)(x+2)
Nico wanted to determine the number of students in his school who buy school lunch. He walked around the cafeteria one lunch period looking to see whether every fifth person in the cafeteria purchased lunch or brought their own. Which method did he use to collect his data? survey simulation experiment observational study
observational study
The graph shows f(x) = and its translation, g(x). Which describes the translation of f(x) to g(x)? translation of four units up translation of five units up translation of four units to the right translation of five units to the right
translation of four units up
An account is opened with $7,595.96 with a rate of increase of 2% per year. After 1 year, the bank account contains $7,746.90. Assuming no deposits or withdrawals are made, which equation can be used to find y, the amount of money in the account after x years? (Round money values to the nearest penny.) y = 7,746.90(1.02)x y = 7,746.90(0.02)x y = 7,595.96(1.02)x y = 7,595.96(0.02)x
y = 7,595.96(1.02)x
The graph of the piecewise function f(x) is shown. What is the range of f(x)? {f(x)| -∞ <f(x) < ∞} {f(x)| -∞ <f(x) ≤ 4} {f(x)|4<f(x)<∞} {f(x)|0≤f(x)<∞}
{f(x)| -∞ <f(x) ≤ 4}
On the coordinate grid, the graph of is shown. It is a reflection and translation of . What is the range of the graphed function? {x |-2 < x < 2} {y |-2 < y < 2} {x | x is a real number} {y | y is a real number}
{y | y is a real number}
The graph of the piecewise function f(x) is shown. What is the range of f(x)? {x | −2 ≤ x < 4} {x | −2 < x ≤ 4} {y | −5 < y < −1} {y | −5 ≤ y ≤ −1}
{y | −5 ≤ y ≤ −1}
Which describes the range of the parent absolute value function? {y | y is a real number} {y | y is an integer} {y|y > 0} {y|y < 0}
{y|y > 0}
The graph shows a vertical translation of y = . What is the range of the translated function? {y|y < 0} {y|y ≥ 0} {y|y is a natural number} {y|y is a real number}
{y|y is a real number}
Which is the graph of f(x) = ?
D
Which is the graph of g(x)? g(x) =
D
Which is the graph of y = 3/x+1 -2?
D
Which statement is true about the function f(x)= ? The domain of the graph is all real numbers. The range of the graph is all real numbers. The domain of the graph is all real numbers less than or equal to 0. The range of the graph is all real numbers greater than or equal to 0.
The range of the graph is all real numbers greater than or equal to 0.
Which statement best describes and the parent function ? The domains of g(x) and f(x) are the same, but their ranges are not the same. The ranges of g(x) and f(x) are the same, but their domains are not the same. The ranges of g(x) and f(x) are the same, and their domains are also the same. The domains of g(x) and f(x) are the not the same, and their ranges are also not the same.
The ranges of g(x) and f(x) are the same, and their domains are also the same.
The function f(x) is to be graphed on a coordinate plane. f(x) = At what point should an open circle be drawn? (-1, 0) (0, 0) (0, 1) (1, 0)
(0, 0)
Chelsea is graphing the function f(x) = 20()x. She begins by plotting the initial value. Which graph represents her first step?
C
Consider the three functions below. f(x) = g(x) = h(x) = Which statement is true? The range of h(x) is y > 0. The domain of g(x) is y > 0. The ranges of f(x) and h(x) are different from the range of g(x). The domains of f(x) and g(x) are different from the domain of h(x).
C
Which function represents a reflection of f(x) = (4)x across the y-axis? g(x) = g(x) = (4)x g(x) = (4)-x g(x) = (4)-x
D
Justin packed two suitcases for his trip and compared the weights of the items he packed in each of the suitcases. Which statement is true about the box plots? The data for suitcase 1 have an outlier, but the data for suitcase 2 does not. The data for suitcase 2 have a greater median than the data for suitcase 1. The data for suitcase 1 has a greater interquartile range than the data for suitcase 2. The data for suitcase 2 has a greater range than the data for suitcase 1.
The data for suitcase 1 have an outlier, but the data for suitcase 2 does not.
The graph of f(x)=3/x+8 is shown. Which statement is true? The function is only increasing when x ≥ −8. The function is only increasing when x ≥ 0. The function is always decreasing. The function is always increasing.
The function is always increasing.
How are the graphs of the functions f(x) = and g(x) = related? The functions f(x) and g(x) are equivalent. The function g(x) increases at a faster rate. The function g(x) has a greater initial value. The function g(x) decreases at a faster rate.
The functions f(x) and g(x) are equivalent.
The function h(x) is defined as shown. h(x) = What is the range of h(x)? -∞ < h(x) < ∞ h(x) ≤ 5 h(x) ≥ 5 h(x) ≥ 3
h(x) ≤ 5
Which value is in the domain of f(x)? f(x) = -7 -6 4 5
4
The graph represents the function f(x) = 10(2)x. How would the graph change if the b value in the equation is decreased but remains greater than 1? Check all that apply. The graph will begin at a lower point on the y-axis. The graph will increase at a faster rate. The graph will increase at a slower rate. The y-values will continue to increase as x-increases. The y-values will each be less than their corresponding x-values.
c, d The graph will increase at a slower rate. The y-values will continue to increase as x-increases.
What are the domain, range, and asymptote of h(x) = (0.5)x - 9? domain: {x | x > 9}; range: {y | y is a real number}; asymptote: y = 9 domain: {x | x > -9}; range: {y | y is a real number}; asymptote: y = -9 domain: {x | x is a real number}; range: {y | y > 9}; asymptote: y = 9 domain: {x | x is a real number}; range: {y | y > -9}; asymptote: y = -9
domain: {x | x is a real number}; range: {y | y > -9}; asymptote: y = -9
Which function represents g(x), a reflection of f(x) = (3)x across the y-axis? g(x) = 2(3)x g(x) = −(3)x g(x) = (3)−x g(x) = 2(3)−x
C
What is the vertex of the graph of f(x) = |x + 5| - 6? (-6, -5) (-6, 5) (-5, -6) (5, -6)
(-5, -6)
The table represents an exponential function. What is the multiplicative rate of change of the function?
B
What are the domain, range, and asymptote of h(x) = 6x - 4? domain: {x | x is a real number}; range: {y | y > 4}; asymptote: y = 4 domain: {x | x is a real number}; range: {y | y > -4}; asymptote: y = -4 domain: {x | x > -4}; range: {y | y is a real number}; asymptote: y = 4 domain: {x | x > 4}; range: {y | y is a real number}; asymptote: y = -4
B
A conditional relative frequency table is generated by row from a set of data. The conditional relative frequencies of the two categorical variables are then compared. If the relative frequencies are 0.48 and 0.52, which conclusion is most likely supported by the data? There is likely an association between the categorical variables because the relative frequencies are similar in value. An association cannot be determined between the categorical variables because the relative frequencies are similar in value. An association cannot be determined between the categorical variables because the relative frequencies are not similar in value. There is likely an association between the categorical variables because the relative frequencies are both close to 0.50.
There is likely an association between the categorical variables because the relative frequencies are similar in value.
Which describes how to graph by transforming the parent function? Translate the parent function 5 units to the left and 7 units up. Translate the parent function 5 units to the right and 7 units up. Translate the parent function 5 units down and 7 units to the right. Translate the parent function 5 units up and 7 units to the right.
Translate the parent function 5 units to the right and 7 units up.
A piecewise function f(x) is defined as shown. f(x) = Which table could be used to graph a piece of the function?
D
An account with a $250 balance accrues 2% annually. If no deposits or withdrawals are made, which graph can be used to determine approximately how many years will it take for the balance to be $282?
D
What is the simplified form of ? 200x10 200x50 20x10 20x50
D
The dot plot represents the amount of rain recorded by rain gauges in different locations around a city. How many rain gauges recorded rainfall? 2 8 11 16
16
Which is equivalent to ? 3 6 9 12
9
UNIT TEST
92%
Which is the graph of f(x) = 100(0.7)x?
A
Which statements accurately describe the function f(x) = 3? Select three options. The domain is all real numbers. The range is y > 3. The initial value is 3. The initial value is 9. The simplified base is .
A, C, E The domain is all real numbers. The initial value is 3. The simplified base is .
Which function represents g(x), a reflection of f(x) = 6 across the y-axis? g(x) = −6 g(x) = −6 g(x) = 6(3)x g(x) = 6(3)−x
C
Which graph represents exponential decay?
C
Which graph shows a negative correlation?
C
Which is equivalent to ?
C
Which is the graph of g(x) = - 2?
C
The function f(x) = 5 is reflected over the y-axis. Which equations represent the reflected function? Select two options. f(x) = f(x) = f(x) = 5 f(x) = 5(5)x f(x) = 5(5)-x
C, D f(x) = 5 f(x) = 5(5)x
Which is the graph of f(x)=3 (2/3)^x?
D
Which statement is true about the polynomial 3j4k−2jk3+jk3−2j4k+jk3 after it has been fully simplified? It has 2 terms and a degree of 4. It has 2 terms and a degree of 5. It has 1 term and a degree of 4. It has 1 term and a degree of 5.
D
f(x) = g(x) = - 3 Which statement about f(x) and its translation, g(x), is true? The range of g(x) is , {y | y > 0} and the range of f(x) is {y | y > -3}. The range of g(x) is , {y | y > 3} and the range of f(x) is {y | y > 0}. The asymptote of g(x) is the asymptote of f(x) shifted three units down. The asymptote of g(x) is the asymptote of f(x) shifted three units up.
The asymptote of g(x) is the asymptote of f(x) shifted three units down.
What are the domain, range, and asymptote of h(x) = (1.4)x + 5? domain: {x | x is a real number}; range: {y | y > 5}; asymptote: y = 5 domain: {x | x > 5}; range: {y | y is a real number}; asymptote: y = 5 domain: {x | x > -5}; range: {y | y is a real number}; asymptote: y = -5 domain: {x | x is a real number}; range: {y | y > -5}; asymptote: y = -5
domain: {x | x is a real number}; range: {y | y > 5}; asymptote: y = 5
Alejandro wants to determine the average shoe size of all of the male students in his school. Which sample is likely to yield the most biased results? every tenth boy on the school's phone list every member of the boys' basketball team every boy in a randomly selected ninth-, tenth-, eleventh-, and twelfth-grade gym class every fifth boy who walks through the front doors of the school in the morning
every member of the boys' basketball team
Which is the graph of the piecewise function f(x)? f(x) =
A
