algebra 1b - unit 3: using functions

which points are part of the solution set of the system shown in the graph? select all that apply.

(-1, -6) (-2, -4)

factor: 4b^2 − 12b + 9

(2b − 3)^2

examine the following function. f(x) = 8x^2 + 2x − 15 what are the factors of the function?

(4x − 5)(2x + 3)

the graph shows the following system of inequalities. {y >= 1/2x , y < 2^x - 3} which of the following points are part of the solution set of the given system? select all that apply.

(5, 7) (-9, -4)

which statements about the functions are true?

(i'm not very good on these so i just guessed, sorry.)

examine the following equation. x^2 + 8x − 9 = 0 using the quadratic formula, which options are solutions to the equation? select all that apply.

1, -9

the height of an object launched into the air can be modeled by the graph shown. what is the maximum height, in feet, the object reaches?

16

examine the following function. f(x) = 2x^2 − 24x + 54 what are the factors of the function?

2(x − 3)(x − 9)

based on the information in the graph, how many dollars are earned for every bag of popcorn sold?

3

which two values of x best represent where the two functions are equal?

3, 8

use the functions to answer the question. f(x) = x^2 + 13 , g(x) = 12x − 14 at what values of x do the functions intersect? select all that apply.

3, 9

malik is buying a guinea pig. the guinea pig comes with a cage and food bowls for $125.00. the expenses for feeding and caring for the guinea pig are $18.00 each month. how much will it cost malik to buy and care for the guinea pig for one year?

341

examine the following equation. 2x^2 − 5x − 7 = 0 which expression can be used to find the solutions to the equation?

5 ± √81/4

use the functions to answer the question. f(x) = 2/7x - 5 g(x) = -4x + 25 at what value of x do f(x) and g(x) intersect?

7

what should be added to both sides of the equation below to complete the square? x^2 + 6x = −8

9

which statements are true?

a solution to f(x) = g(x) is 4. a solution to f(x) = g(x) is -2. solutions to f(x) = g(x) can be found where the functions intersect.

lesson 11

applying functions

which letter is located within the solution set of the system, a, b, or c?

b

which sister will have more seashells after 10 weeks of collecting? explain.​

belinda, b(x), because her collection is increasing as an exponential function.

a researcher determined the amount of ducks that were in a pond over a four-year time span. the results are shown in the table below. select an equation that best models the amount of ducks (d) that will be in the pond during the nth year.

d = 14n + 50

the temperature of a mixture is decreasing by 5c every hour. when it was first mixed, its temperature was recorded at -20c. which answer correctly represents the temperature of the mixture over time?

f(x) = -5x - 20

a certain type of cell can double itself every hour, because it has a growth factor of 2. a laboratory has 15 of these cells. which function best models the amount of cells in the laboratory after x hours?

f(x) = 15 * 2^x

students observing a caterpillar crawl on a tree noticed that the caterpillar crawled upwards 3/8 of an inch every minute. the caterpillar was already 4.5 feet off the ground when the students began observing. which function represents the height of the caterpillar above the ground in inches after x minutes?

f(x) = 3/8x + 54

each day, a zoo sells 8400 special admission passes to visitors. the passes allow these visitors to enter the park early. the number of visitors who pay the normal entry fee has been decreasing by 7% each day. today, 56,000 visitors paid the normal entry fee. which function represents what the total number of visitors to the zoo will be after x days?

f(x) = 56,000(0.93)^x + 8400

the graph below shows the solution for the following system. {f(x) = 2x − 3 , g(x) = 2x − 4} which statements are true? select all that apply.

f(x) = g(x) when x = 0. x = 0 is a solution to the system. when x ≈ 2.7, the graphs of f(x) and g(x) intersect because they are equal to each other at that value.

which of the following statements are true?

f(x) has a minimum at −5, and it opens up to positive infinity. g(x) goes to positive infinity in the positive domain, so there is no maximum value. g(x) has a horizontal asymptote at y = −5, so the minimum is almost at −5 for any negative, noninfinite interval. f(x) has a smaller minimum than g(x) over the interval −6 ≤ x ≤ 2, because g(x) will never intercept its asymptote.

which function has the greater maximum value, f(x) or g(x)?

g(x)

examine the following equation. f(x) = x^2 − 2x − 8 which option shows the graph of the equation?

https://cdstools.flipswitch.com/asset/media/1069586

for an experiment, students built mousetrap catapults to launch eraser caps. a cap is launched from a mousetrap on the floor. its height is modeled by this equation, where x is time in seconds and f(x) is height in feet. which graph represents this situation?

https://cdstools.flipswitch.com/asset/media/1069698

which is the graph of y = −1/2(x − 3)^2 − 1?

https://cdstools.flipswitch.com/asset/media/1069715

which option shows the solution to the system?

https://cdstools.flipswitch.com/asset/media/1072463

examine the following system of inequalities. {y < -1/4x + 4 , y > (x + 4)^2 } which option shows the graph of the system?

https://cdstools.flipswitch.com/asset/media/1072954

consider the following function. f(x) = √2x - 1 which graph correctly displays the function?

https://cdstools.flipswitch.com/asset/media/1073973

consider the following function: f(x) = −3(3)√x which graph correctly displays the function?

https://cdstools.flipswitch.com/asset/media/1073983

a child tosses a bean bag from the ground. its path is modeled by the following equation, where x is time in seconds and f(x) is height in feet. which graph shows the quadratic function that represents this situation?

https://cdstools.flipswitch.com/asset/media/1155386

which option shows the graph of the system?

https://cdstools.flipswitch.com/asset/media/1155453

which option shows the graph of the system?

https://cdstools.flipswitch.com/asset/media/1155458

examine the following system of inequalities. {y > -x + 4 , y <= -(1/2)^x + 6} which graph shows the solution to the system?

https://cdstools.flipswitch.com/asset/media/1155475

consider the following function. f(x) = −3/4 |x − 2| + 5 which graph correctly displays the function?

https://cdstools.flipswitch.com/asset/media/1155487

consider the following function. f(x) = 2|x + 3| − 6 which graph correctly displays the function?

https://cdstools.flipswitch.com/asset/media/1155490

consider the following function. f(x) = −2√x-3 + 5 which graph correctly displays the function?

https://cdstools.flipswitch.com/asset/media/1155502

consider the following function. f(x) = 2 (3)√x−3 which graph correctly displays the function?

https://cdstools.flipswitch.com/asset/media/1155508

kala was hired to finish painting the exterior of a house. she created the function f(x) = 80x + 60 to represent how many square feet of the house will be painted, f(x), based on how many hours she spends painting, x. what is the correct interpretation of the parameters of this function?

kala points at a rate of 80 ft^2 per hour. before she was hired, 60 ft^2 were already painted.

which line contains oliver's first mistake?

line 2

luis and sara both open savings accounts at the same bank. luis opens his account with $125 and deposits $60 per week. sara opens her account with $50 and increases the amount by 4% per week. which account has a greater average rate of change between 10 and 20 weeks?

luis's account has a greater average rate of change than sara's account between 10 and 20 weeks.

lesson 14

more than one function (or relation)

lesson 15

other types of functions

lesson 13

problem solving with functions

lesson 12

quadratic functions

a kayak rental company charges $25.00 to rent a kayak and $3.50 for each half hour it is used. which linear function best represents the total cost of renting a kayak for 4 hours?

r(t) = 3.50t + 25 f(8) = 53

a movie theater observes that on saturdays, the number of soda cups it has decreases by about 1/5 of the initial value every hour. each saturday morning, the movie theater stocks 1250 cups. rosalia and monica work at the movie theater this saturday. monica says that there will be 1000 cups left after 4 hours because 1250(1/5) * 4 = 1000. rosalia says this is not right and that there will be 250 cups left after 4 hours. which of the following statements are true? select all that apply.

rosalia is correct. the equation f(x) = 1250 - 250x gives the correct number of cups left after x hours. rosalia is correct. after the first hour, there will be 1000 cups left. after the second hour, there will be only 250 cups left after 4 hours.

what is the next step luna should take? explain.

set the factors equal to 0; use the zero product property.

the model for an investment that compounds interest annually is: b(t) = 10,000(1.07)^t. based on this model, which statements are true?

the annual interest rate is 7% the principal investment is $10,000. after 10 years, the value of the investment will be approximately double the starting value.

which has the greater average rate of change over the interval 0 ≤ x ≤ 4, the bacteria or the fungus? explain.

the bacteria have the greater average rate of change, because the average rate of change of the bacteria is 9.5, and the average rate of change of the fungus is 8.

a flock of birds is flying south, toward the equator, at an hourly rate. a scientist created the function f(x) = -60x + 1320 to represent how many miles away from the equator the birds are after a given number of hours. which of the answers are true of the scenario represented by this function?

the birds began 1320 miles from the equator. the birds are flying toward the equator at a rate of 60 mph.

which statements are true about the domain of the graph? select all that apply.

the domain of the graph is 0 ≤ x ≤ 36 the largest value in the domain is 36, because after 36 hours there will be no more pounds of pecans remaining in the store

certain bacteria can grow in extreme temperatures, including temperatures below 0∘ celsius. the relationship between the temperature and the rate of bacteria growth is shown in the following graph. the x-values show the degrees, in celsius, and the y-values show the growth rate in multiples per hour. which statements are true? select all that apply.

the horizontal asymptote of the function is y = 2. the growth rate of the bacteria will always be greater than 2 multiples per hour.

consider a sample of some of the points from the graph of the quadratic function f(x), shown in the following table. also examine the following graph, which shows the parabola of g(x) only one of the following statements is completely correct. which one is it?

the maximum value of f(x) is greater than the minimum value of g(x).

which statement is completely correct?

the minimum value of f(x) is greater than the maximum value of g(x).

a scientist is studying bacteria and records the number of bacteria over time. the scientist determines that the function n(t) = 300(1.30)^t models the number of bacteria, n, after t hours. which statement correctly interprets this model?

the number of bacteria is originally 300 and increases by 30% every hour.

a car depreciates according to the model v(t) = 19,000(0.719)^t + 700. based on this model, which statements are true?

the original value of the car was $19,700. the approximate value of the car will never drop below $700. the approximate depreciation rate is about 28.1% per year.

a local store is having a sale on pecans. the following graph shows the number of remaining pounds of pecans for every hour during the sales event. what is the rate of change in the graph, and what does it mean in this situation?

the rate of change is −1/2, which means that the store's supply of pecans is decreasing by 1 pound every 2 hours.

the following graph models an amusement park ride that shows its height from the ground during several seconds of a ride. which statement is true?

the ride starts on the ground, reaches its highest point at 7 seconds, then ends on the ground after 14 seconds.

the following graph models an amusement park ride that shows its height in yards from the ground during several seconds of a ride. which statement is true?

the top of the ride is about 10 yards above the ground.

tyler and daniel each deposited money into different banks with different savings plans. tyler went to bank 1 and deposited $500. daniel went to bank 2 and deposited $1500. the graph above shows how much money is in each savings account after 14 years. according to the graph, who will have more money by year 20, and why?

tyler, because his money is increasing exponentially.

the value of a comic book has been increasing over time. each year, the value increases by 30%. the original cost of the comic book was $4.00. which function models the value of the comic book after n years?

v(n) = 4(1.3)^n

consider the following function. f(x) = 4/3 |x + 2| − 5 which table shows values that are all true for the function?

x : -14, -11, -8, -5, -2, 1, 4, 7, 10 f(x) : 11, 7, 3, -1, -5, -1, 3, 7, 11

consider the following function. f(x) = √x + 5 which table is the correct table of values for the function?

x : -5, -4, -1, 4 f(x) : 0, 1, 2, 3

consider the following function. f(x) = −4 (3)√x + 6 which table shows correct values for the function?

x : -8, -1, 0, 8 f(x) : 14, 10, 6, -2

consider the following function. f(x) = −√1/2x - 7 which table is the correct table of values for the function?

x : 0, 2, 8, 18 f(x) : -7, -8, -9, -10

the equations y = x^2/2 − 8 and y = 2x − 2 are graphed below. what are the solutions to the equation x^2/2 − 8 = 2x − 2?

x = -2 and x = 6

examine the following equation. 0 = −3x^2 + 5x + 9 which answer can be used to find the solutions to the equation using the quadratic formula?

x = −5 ± √133/−6

factor: x^3 − 2x^2 − 8x

x(x − 4)(x + 2)