Analyzing Compositions of Functions — Unit test Answers

Let and . What are the domain and range of ?

Maryanne throws a ball off the top of a building. The table shows the height of the ball in feet, f(t), at t seconds.

Choose the function that represents the data in the table.

A factory produces 1,250,000 toys each year. The number of toys is expected to increase by about 150% per year. Which model can be used to find the number of toys, n (in millions), being produced in t years?

The graph shows the best-fit regression model for a set of data comparing the number of hours spent hiking and the number of miles traveled in one day.

Scientists studied a deer population for 10 years. They generated the function f(x) = 248(1.15)x to approximate the number of deer in the population x years after beginning the study. About how many deer are in the population 3 years after beginning the study?

The graph below represents c, the amount a phone company charges, based on m, the number of minutes the customer uses each month. If there are a maximum of 44,640 minutes in a month, which equation best represents the phone company’s monthly charges?

Error

A modern art piece includes drops of paint spilling periodically into a basin of liquid. The display is timed with an expectation that the circular area of the green spill increases 1.5 square centimeter per hour. Increase in area: A(h) = 1.5h; h in hoursIncrease in diameter: in square centimeters

When estimating a job to bid, a contractor’s estimator first determines the actual cost of labor using the functionL(h) = 28.75h, where h is the number of estimated hours it will take to complete the job. Next, the estimator adds the labor burden, which accounts for taxes and insurance, using the function B(L) = 1.78L. Finally, the estimator calculates the selling price, including the markup for overhead and profit, using the function M(B) = 1.43B.

Daniel is on an airplane flying to a destination 825 miles away. After one hour, the pilot announces that the plane is 495 miles away from its destination airport. In another hour, the pilot announces that the plane will begin its half-hour descent for the final 165 miles.

If , , and , what is ?

A store uses the expression –2p + 50 to model the number of backpacks it sells per day, where the price, p, can be anywhere from $9 to $15. Which price gives the store the maximum amount of revenue, and what is the maximum revenue? (Revenue = price number of backpacks.)

The function C(L) = |L – 105| can be used to determine the difference between the expected and actual crop of lemons, L, from a single tree. The estimated total weight in pounds of number of lemons can be modeled by the function w(L) = 0.25L.

The table shows the circumference of a tree in centimeters, y, at x years.Choose the function that represents the data.

The height of a toy rocket that is shot in the air with an upward velocity of 48 feet per second can be modeled by the function , where t is the time in seconds since the rocket was shot and f(t) is the rocket’s height in feet. What is the maximum height the rocket reaches?

Environmentalists estimate an annual population decrease of giraffes in the wild of 3.5% due to development. This can be modeled by the function p(x) = 140,000(0.965)x, where x is the number of years of tracking the populations. Conservationists have developed a sanctuary that has shown the ability to increase the population by 0.85% per year. The increase can be modeled by the function S(p) = p(1.0085)x.

The table shows the estimated number of lines of code written by computer programmers per hour when x people are working.