PSAT/NMSQT Prep 2022 - Eggert M.D., Strelka A. 2022

How much have you learned?
Functions
Passport to advanced math

Directions: For testlike practice, give yourself 15 minutes to complete this question set. Be sure to study the explanations, even for questions you got right. They can be found at the end of this chapter.

17. A function is defined by the equation For what value of x does f(x) = 5?

A. −5

B.2

C.9

D. 30

18. If f(x) = -x + 5 and g(x) = x², which of the following is NOT in the range of f (g(x))?

A. −11

B.0

C.1

D. 9

19. The graph of the function f(x) is shown above. What is the domain of the function?

A. y ≥ −4

B.All real numbers

C.y > −4

D. The domain is undefined.

20. Jayesh is a 150-pound, 5-foot-10-inch, 18-year-old male, and he requires 2,048 calories per day to maintain his weight when he doesn’t exercise. When he plays basketball, he burns 231 additional calories per hour. Assuming he wants to maintain his current weight, how many more calories per day does he require if he plays basketball for four hours instead of two hours?

21. Two functions are defined as follows: and . What is the value of g(f(x)) when x = 2?

A. 6

B.12

C.34

D. 36

22. The point (3, 6) lies on the graph of function f in the xy-plane. If then what is the value of k?

23. A scientist is studying the average annual growth of trees in a newly planted forest. The average height of the trees was 3.6 feet when they were planted, and they have grown an average of 2.4 feet per year since then. The scientist has been studying the growth of the trees for five years. If she uses the function g(y) = h + 2.4(y), where h is the height (in feet) of the trees five years after they were planted and y is the number of years after the fifth year, to determine the expected further growth of these trees from the sixth year onward, which of the following would be included in the range of the scientist’s results?

A. 6

B.10.8

C.15.4

D. 18

24. If and what is f (g(x))?

A. x + 1

B.2x + 2

C.4x + 1

D. 4x + 4

25. The functions f(x) and g(x) are graphed in the xy-plane above. What is the value of f (−2) − g(2)?

A. −30

B.−20

C.−15

D. 20

26. To install fencing, a builder charges $15 per foot for the first 100 feet plus an additional $12 per foot thereafter. If c represents the total cost of a fence installation, in dollars, and x represents the length of the fence in feet, then which of the following functions best describes the cost of a fence that is more than 100 feet long?

A.

B.

C.

D.

27. The complete graph of the function f(x) in the xy-plane is shown above. What is the domain of f(x)?

A. All real numbers greater than −5

B.All real numbers between and including −5 and 3

C.All real numbers between and including −3 and 3

D. All real numbers