Modeling with Functions — Test Answers

Choose the function represented by the data.

Which range of time values describes the entire interval over which she would be interpolating?

What is the range of open paren f circ g close paren times x ?

The equation f of b is equal to 288 minus 12 b models the function represented in the table. What are the restricted domain and range of the function?

Which is most likely true of the data set represented by the regression model on the graph?

Let f of x is equal to e to the x th power and g of x is equal to x minus 3 What are the domain and range of open paren f circ g close paren times x ?

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

The table shows some values of a function of the form y is equal to A x squared plus b x plus c x 3 4 5 6 7 y negative 10 negative 16 negative 24 negative 34 negative 46

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 f of t is equal to negative 16 t squared plus 48 t , where t is the time in seconds since the rocket was shot and f of t is the rocket’s height in feet. What is the maximum height the rocket reaches?

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

If f of x is equal to the fraction with numerator x plus 4 and denominator x , g of x is equal to x minus 2 , and h of x is equal to 4 x minus 1 , what is open paren f circ h circ g close paren times x ?

The function cap c times cap l is equal to start absolute value cap l minus 105 end absolute value can be used to determine the difference between the expected and actual crop of lemons, cap l , from a single tree. The estimated total weight in pounds of number of lemons can be modeled by the function w times cap l is equal to 0 point 2 5 liters Which function can be used to find the estimated weight difference between the expected crop and the actual crop depending on the number of lemons harvested?

Scientists studied a deer population for 10 years. They generated the function f of x is equal to 248 times 1 point 1 5 to the x th power 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?

When estimating a job to bid, a contractor’s estimator first determines the actual cost of labor using the function cap l times h is equal to 28 point 7 5 h , 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 cap b times cap l is equal to 1 point 7 8 liters Finally, the estimator calculates the selling price, including the markup for overhead and profit, using the function cap m times cap b is equal to 1 point 4 3 cap b Which composite function can be used to find the selling price for the labor portion of a bid based on the estimated number of hours?

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. Which equation represents the remaining distance, in miles, to the destination in terms of t , the time, in hours, since leaving the airport?

If f of x is equal to 1 over x and g of x is equal to x plus 4 , which of the following is the graph of open paren g circ f close paren times x ?

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 point 5 square centimeter per hour. Increase in area: cap A times h is equal to 1 point 5 h ; h in hours Increase in diameter: d times cap A is equal to square root of cap A over pi end root ; cap A in square centimeters The artist would like to know the area of the spill after any number of hours, h Which composite function represents the diameter of the green paint as a function of hours?

If a flowering tree is cared for properly, the number of blossoms produced on the tree will exponentially increase until the tree reaches maturity. Which graph could show y , the number of blossoms expected on a flowering tree, for each year after the young tree is planted, x ?

The table shows the circumference of a tree in centimeters, y , at x years. x 0 5 10 15 20 25 y 0 13 point 5 27 40 point 5 54 67 point 5 Choose the function that represents the data.

What type of function is represented?