Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{x-2}$$?

Accepted Answer

$$[2, \infty)$$

Question 2

A car was purchased for $$22,500 and its value decreases by 3$$,200 per year for the first seven years. Which function correctly models the value $$V(t) of $$the car after $$t$$ years, where $$0 \leq t \leq 7$$?

Accepted Answer

$$V(t) = 22,500 - 3,200t$$

Question 3

Which of the following statements about functions is TRUE?

Accepted Answer

The range of a function is the set of all possible output values.

Question 4

Given the function $$f(x) = x^2$ + 3x - 4$$, what is the value of $$f(-2)$$?

Accepted Answer

$$-2$$

Question 5

Which of the following graphs passes the Vertical Line Test and therefore represents a function?

Accepted Answer

A parabola opening upwards

Question 6

For the piecewise function $$f(x) = \begin{cases} x+2 & x \u003c 0 \ 3x & x \geq 0 \end{cases}$$, what is $$f(-3)$$?

Accepted Answer

$$-1$$

Question 7

A postal rate function charges $$0.78$$ for up to 1 ounce, $$1.07$$ for up to 2 ounces, $$1.36$$ for up to 3 ounces, and $$1.65$$ for up to 3.5 ounces. What is the domain of this function?

Accepted Answer

$$[0, 3.5]$$

Question 8

Given $$f(x) = 2x - 5$$, what is the difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$2$$

Question 9

Which of the following is NOT a valid way to define a function?

Accepted Answer

By assigning multiple outputs to a single input

Question 10

For the function $$f(x) = \frac{1}{x-3}$$, what is the domain?

Accepted Answer

$$(-\infty, 3) \cup (3, \infty)$$

Question 11

If the graph of a function $$f$$ crosses the y-axis at $$(0, 5)$$, what is the y-intercept of $$f$$?

Accepted Answer

$$5$$

Question 12

Which scenario best illustrates a piecewise-defined function?

Accepted Answer

A tax rate that changes at different income levels

Question 13

Given $$f(x) = x^2$, what is the difference quotient $$\frac{f(x+h) - f(x)}{h}$$ simplified?

Accepted Answer

$$2x + h$$

Question 14

Which of the following best describes the range of the function $$f(x) = |x|$$?

Accepted Answer

$$[0, \infty)$$

Question 15

For the function $$f(x) = \frac{1}{x}$$, which value is NOT in the domain?

Accepted Answer

$$0$$

Question 16

If $$f(x) = 3x + 2$$, what is the value of $$x$$ where the graph crosses the x-axis?

Accepted Answer

$$x = -\frac{2}{3}$$

Question 17

Which of the following is an example of a dependent variable in a real-world function?

Accepted Answer

The value of a car after $$t$$ years

Question 18

For the function $$f(x) = \sqrt{9 - x}$$, what is the domain?

Accepted Answer

$$(-\infty, 9]$$

Question 19

Which of the following best describes the difference between domain and range?

Accepted Answer

Domain is the set of possible input values; range is the set of possible output values.

Question 20

If a function is defined by $$f(x) = \frac{1}{x^2$ - 4}$$, which values must be excluded from the domain?

Accepted Answer

$$x = 2$$ and $$x = -2$$

Basics of Functions and Their Graphs

Study Guide - Practice Questions

Study Guide - Flashcards