Question 1

Which of the following best defines a function?

Accepted Answer

A relation where each input is paired with exactly one output.

Question 2

Given the function $$y = \sqrt{x - 5}$$, what is the domain?

Accepted Answer

$$x \geq 5$$

Question 3

If a table lists the year and U.S. sales of personal computers, which is most appropriately considered the domain?

Accepted Answer

The year

Question 4

A graph is a function if:

Accepted Answer

No vertical line intersects the graph at more than one point.

Question 5

Which of the following is NOT a function?

Accepted Answer

$$y^2 = x$

Question 6

Suppose $$y = \frac{2x}{x-3}. $$What is the domain of this function?

Accepted Answer

$$x 
eq 3$$

Question 7

A mathematical model is best described as:

Accepted Answer

A mathematical representation of a real-world situation.

Question 8

If $$f(x) = x^2$ + 5$$, what is the range of $$f$$?

Accepted Answer

$$y \geq 5$$

Question 9

Given the scatter plot of years versus U.S. sales of computers, what does the slope of the best-fit line represent in a real-world context?

Accepted Answer

The average increase in U.S. computer sales per year.

Question 10

If $$y is a $$function of $$x$$, which of the following must be true?

Accepted Answer

Each $$x$$ value corresponds to exactly one $$y$$ value.

Question 11

Suppose the domain of a function is all real numbers except $$x = -2. $$Which of the following could be the equation for the function?

Accepted Answer

$$f(x) = \frac{1}{x+2}$$

Question 12

A function is given by $$f(x) = \sqrt{9 - x^2$}. $$What is the domain of $$f$$?

Accepted Answer

$$-3 \leq x \leq 3$$

Question 13

If a data set shows the number of years since 2000 and the corresponding population, what is the independent variable?

Accepted Answer

The number of years since 2000

Question 14

Which of the following real-world scenarios is best modeled by a function?

Accepted Answer

The temperature at each hour of the day.

Question 15

Given $$f(x) = \frac{1}{x}$$, which of the following statements is true?

Accepted Answer

The function is undefined at $$x = 0.$$

Question 16

If $$y is a $$function of $$P$$, and $$y = 3P + 2$$, which is the dependent variable?

Accepted Answer

$$y$$

Question 17

A function is defined by $$f(x) = \sqrt{x-2}. $$What is the smallest value in the domain?

Accepted Answer

$$2$$

Question 18

Which of the following best describes the range of $$f(x) = x^2$ for all real x$?

Accepted Answer

$$y \geq 0$$

Question 19

If a function models the cost $$C of $$producing $$x$$ items as $$C(x) = 5x + 200$$, what does the 200 represent in a real-world context?

Accepted Answer

The fixed cost of production.

Question 20

Suppose $$f(x) = \frac{x^2$ - 9}{x - 3}. $$What is the domain of $$f$$?

Accepted Answer

$$x 
eq 3$$

Functions, Domain, and Range: Foundations of College Algebra

Study Guide - Practice Questions