PreCal Cul Exam
Find the difference quotient of the function, V(x) =, and use it to find the average rate of change of V as h changes from 10 to 10.05 meters.
, average rate of change from 10 to 10.05 ≈ 2.513 cubic meters per meter
Based on the graph, what is the solution to 2x 3 - 3x 2 ≥ 14x?
-2 ≤ x ≤ 0 or 3.5 ≤ x < ꝏ
Choose the answer that best completes the sentence.
-2- root 3i is a known root.
Which algebraic expression represents the phrase "the quotient of negative eight and the sum of a number and three"?
-8/g+3
If 9i is a root of the polynomial function f(x), which of the following must also be a root of f(x)?
-9i
Identify all of the root(s) of g(x) = (x2 + 3x - 4)(x2 - 4x + 29).
1 -4 2+5i 2-51
What are the coefficients for the binomial expansion of (p + q)6?
1, 6, 15, 20, 15, 6, 1
Given and c is a real number, what is the multiplicative inverse of
1/4c+5
Which of the following is equivalent to 36^1/2?
1/6
Which expression represents the fourth term in the binomial expansion of (e + 2f)10?
10C3(e7)(2f)3
What is the coefficient of the x5y5-term in the binomial expansion of (2x - 3y)10?
10C5(2)5(-3)5
Which expression represents the sixth term in the binomial expansion of (2a - 3b)10?
10C5(2a)5(-3b)5
The following list gives the coefficients for the binomial expansion of (x + y)10. What is the value of B?
120
Which of the following is equivalent to RootIndex 5 StartRoot 13 cubed EndRoot?
13^3/5
What is the coefficient of the third term in the binomial expansion of (a + b)6?
15
Function K(v) represents the kinetic energy, in joules, of an object with a mass of 20 kilograms traveling with velocity v meters/second (m/s). The difference quotient of K(v) is 20v + 10h. What is the average rate of change in kinetic energy of an object as the velocity increases from 5 m/s to 12.5 m/s?
175 joules per m/s
The annual profits of a company are modeled by the function f(x) = x4 - 87x2 - 26x + 2680, where f(x) represents an amount in thousands of dollars, and x is years, starting in 1950. During what years has the company had profits of one million dollars or more?
1950 to 1955, and 1958 to the present
Solve the inequality and write the solution in interval notation:
(-1.1)U(2,infinity)
Solve the inequality and write the solution in interval notation:
(-5, 6)
Which set of ordered pairs could be generated by an exponential function?
(0, 1), (1, 3), (2, 9), (3, 27)
The amount of water leaking from a water tank can be modeled with the function f(x) = −x3 − 10x2 − x + 120, where x measures the number of minutes since the leak began and f(x) measures the volume of the tank. During what time period is there water in the tank?
(0, 3)
The amount of algae in a bloom, P, can be modeled by the equation P = t4 + 6t3 + 7t2 + 8t, where t is measured in weeks. During what interval of t will the population of algae be greater than 500?
(0.3452, ∞)
The volume of a rectangular prism with a length of x meters, a width of x − 1 meters, and a height of x + 11 meters is no more than 180 cubic meters. What are the possible values of the length?
(1, 4)
An aquarium has dimensions 2x feet, (x - 1) feet, and (x + 2) feet. The aquarium volume must be no more than 280 cubic feet.
(1, 5]
The perimeter of a rectangle is 60 meters. What are the possible lengths of any of the rectangle's sides if its area exceeds 216 square meters?
(12, 18)
Which interval(s) represent possible lengths, in feet, for the horizontal edges of the garden?
(20-10root2,10)U(30,20+10root20) D.
What is the solution of the following quadratic inequality? 9x - x2 > 18
(3, 6)
What is the product? 6(x^2-1)6x-1/6(x+1)
(x - 1)(6x - 1)
Which expression is equivalent to (StartFraction 4 Superscript five-fourths Baseline time 4 Superscript one-fourth Baseline Over 4 Superscript one-half baseline EndFraction) Superscript one-half?
2
How many x-intercepts appear on the graph of this polynomial function?
2 x-intercepts
Which algebraic expression represents the phrase "two times the quantity of a number minus 12"?
2(y -12)
The sound intensity of rustling leaves is 100 times the reference intensity. Use your graph to determine the sound intensity of rustling leaves in decibels.
20
Which set of numbers is correctly ordered from least to greatest?
24pi/5, 63/4, 15.758, 956roote
What is the solution of x4 - 3x3 + x2 + 3x - 2 < 0?
What is the solution of x4 - 3x3 + x2 + 3x - 2 < 0?
Which of the following is the expansion of (2m - n)7?
Which of the following is the expansion of (2m - n)7?
Which of the following is equivalent to (5)^7/3?
^3root5^7
Which graph shows a polynomial function of an even degree?
a
Which graph shows a polynomial function with a negative leading coefficient?
a
Finding which number supports the idea that the rational numbers are dense in the real numbers?
a terminating decimal between -3.14 and -3.15
Which best describes the graph of f(x) = log2(x + 3) + 2 as a transformation of the graph of g(x) = log2x?
a translation 3 units left and 2 units up
Identify the horizontal asymptote of each graph. t(x)=6^x
y = 0
For the function f(x) = -x + 21, what is the difference quotient?
−1; h ≠ 0
The equation T squared = A cubed shows the relationship between a planet's orbital period, T, and the planet's mean distance from the sun, A, in astronomical units, AU. If planet Y is twice the mean distance from the sun as planet X, by what factor is the orbital period increased?
2^3/2
According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function?(9x + 7)(4x + 1)(3x + 4) = 0
3
Which of the following describes the roots of the polynomial function ?
3 with multiplicity 4 and -6 with multiplicity 2
How many x-intercepts appear on the graph of this polynomial function?
3 x-intercepts
What is the quotient? 2m+4/8 +m+2/6
3/2
Stephen wrote out the following steps to compute the difference quotient, v(x) = x3 + 8.
3x2 + 3xh + h2
Adriyana wants to determine the difference quotient
3x2 + 3xh + h2 + 1
Function A(e) represents the surface area of a cube in terms of its edge length, e, and the difference quotient is 12e + 6h. What is the average rate of change in surface area of a cube as the edge length increases from 3 inches to 5 inches?
48 square inches per inch
For the function g(x) = 2x2 - 19, what is the difference quotient?
4x + 2h; h ≠ 0
A store sells bouquets of fruits for $10 a bouquet. The daily cost to produce x bouquets of fruits is defined by the function f(x) = - x 4 + 3x 3 + 5x 2 + 20x + 1.
5
According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function? f(x) = 4x5 - 3x
5 roots
How many turning points are in the graph of the polynomial function?
5 turning points
How many terms are in the binomial expansion of (2x + 3)5?
6
Find the difference quotient of the function, v(x) = -0.5x2 + 6x + 5.
6 - x - 0.5h
What is the coefficient of the x6y3 term in the expansion of (x + 2y)9?
672
According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function?
7 roots
Which of the following is the expansion of (3c + d2)6?
729c6 + 1,458c5d2 + 1,215c4d4 + 540c3d6 + 135c2d8 + 18cd10 + d12
Which of the following is equivalent to 16 Superscript three-fourths?
8
Which function represents a vertical stretch of an exponential function?
A. f(x)=3(1/2)^x
Which sequence of steps is a correct derivation of the difference quotient for f(x) = 3 - log x?
A....
Which graph shows a polynomial function with a positive leading coefficient?
B
Which function is graphed below? On a coordinate plane, an exponential decay function is shown. The curve starts in quadrant 2 and decreases into quadrant 1. It crosses the y-axis at (0, 3) and approaches y = 0 in quadrant 1.
B. y=(1/3)^x
Which expression is equivalent to x ^ -5/3
C. 1/ ^3rootx^5
Which function has a range of y < 3?
C. y= -(2)^x+3
Find the difference quotient of the rational function, r(t) =- 3/t+6.
D.
What is the difference quotient of the function, ? g(x)= root x x> 0
D.
Which expression represents the difference quotient of the function ?
D.
Which graph represents an exponential function?
D.
What is the end behavior of the graph of the polynomial function y = 7x12 - 3x8 - 9x4?
D. x->-infinity , y -> infinity and as x -> infinity, y -> infinity
Hal makes an error when determining the difference quotient of f(x) = x2 + 11x + 2.
He did not expand (x + h)2 correctly.
If f(x) is a third degree polynomial function, how many distinct imaginary roots are possible?
If f(x) is a third degree polynomial function, how many distinct imaginary roots are possible?
Moira uses a difference quotient to determine the average rate of change of f(x) = x2 + 14x from x = -11 to x = 8.
She substituted incorrectly when evaluating the difference quotient.
The difference quotient is used to determine the average rate of change of g(x) = 5x2 + 6x on the interval from x = 1 to x = 5. Which statement describes the process correctly?
The difference quotient is 10x + 5h + 6, so the average rate of change is 10(1) + 5(4) + 6 = 36.
What are the domain and range of f (x) = (one-fifth) Superscript x?
The domain is all real numbers. The range is all real numbers greater than zero.
Which statement describes how the graph of the given polynomial would change if the term 2x5 is added?y = 8x4 - 2x3 + 5
The ends of the graph will extend in opposite directions.
Which of the following describes the polynomial function?
The function has an odd degree.
How does the graph of y = 3x compare to the graph of y = 3-x?
The graphs are reflected across the y-axis.
How does the graph of y = 3-x compare to the graph of
The graphs are the same.
Which statement about the binomial expansion of (x2 - x)9 is true?
The last term is -x9.
Which statement about the simplified binomial expansion of (a + b)n, where n is a positive integer, is true?
The values of nC0 and nCn are equal to 1.
Which graph shows a polynomial function of an odd degree?
c
What are the domain and range of the function f(x) = 3x + 5?
domain:(-infinity,infinity) ; range:(5, infinity)
Which of the following describes the number and nature of all the roots of this function?
f (x) has three real roots and two imaginary roots.
Two roots of a third degree polynomial function f(x) are -4 and 4. Which statement describes the number and nature of all roots for this function?
f(x) has three real roots.
According to the Fundamental Theorem of Algebra, which polynomial function has exactly 11 roots?
f(x)=(x+2)^3(x^2-7x+3)^4
What are the minimum and maximum values of x, for which x3 + x2 - 6x ≥ 0?
minimum = -3, no maximum
Which number is irrational?
pi/ ^3 root 27
Which of the following describes the transformations of g (x) = negative (2) Superscript x + 4 Baseline minus 2 from the parent function f (x) = 2 Superscript x?
shift 4 units left, reflect over the x-axis, shift 2 units down
Which of the following gives all of the sets that contain ?
the set of all rational numbers and the set of all real numbers
Which set does not contain -3?
the set of all whole numbers
Write the expression 3x + 4 using words. Choose the correct phrase below.
the sum of three times a number and four
Which algebraic expression represents the phrase "six less than a number"?
x - 6
The width of a rectangular prism is five less than the length, and the height of the prism is twice the length. Let x represent the length of the prism.
x ≥ 8.5 units
Which expression is equivalent to x y Superscript two-ninths?
x(^9rooty^2)
Simplify mc001-1.jpg
x/x+3
Which expression is equivalent to RootIndex 3 StartRoot x Superscript 5 Baseline y EndRoot?
x^5/3y1/3
Which expression is equivalent to (x^27y)^1/3?
x^9(^3rooty)
Identify the horizontal asymptote of each graph. t(x)=5^x-3
y = -3
