PSAT Math Multiple-Choice Practice Test 37: Passport to Advanced Math: Functions

1. A biologist studying the birth rate of a certain fish uses the function b(n) to analyze the fish's effect on other parts of the ecosystem, where n is the number of eggs laid by the fish over a given period of time. Which of the following lists could represent the domain for the biologist's function?

2. A book publisher pays writers a base fee of $2,500 for each book that it publishes, plus 5 cents per word. If one of its writers earned $8,000 on her book last year, how many words, w, did she write for the publisher?

3.

Tyree is dropping old pennies into a jar that contains a cleaning solution. As he adds more pennies, the height of the solution in the jar changes based on the number of pennies he adds. The figure shows this relationship after 50 pennies have been dropped in the jar. If the height of the solution in the jar was 5 inches (in) before any pennies were added, which of the following linear functions represents the relationship between the number of pennies, p, and the height in inches, h(p), of the solution in the jar?

4. A teacher is buying supplies for the upcoming school year. Every year, basic classroom supplies such as chalk and paper cost her $500, and she spends an additional $25 per child in her class. The school reimburses her $10 per child for half the children in her class. Which function best describes the amount, in dollars, that the teacher spends per school year on supplies, given that s represents the number of students in the class?

A.

B.

C.

D.

5. An environmental agency is working to reduce the amount of toxic waste that a company discards in the ocean. Currently, the company discards 10.8 -million pounds of toxic waste annually, and the agency's goal is to eliminate that amount by collecting the toxic waste and putting it through a process that makes the substance nontoxic. If the agency increases its processing capacity at a constant rate and meets its goal at the end of the 14th year, which of the following linear functions f could the agency use to model the amount of toxic waste (in millions of pounds) being added to the ocean t years into the -program?

A.

B.

C.

D.

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

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

8.

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

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

10. 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?

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

12.

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

13. 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.

14.

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