$$x \u003e 0$$ and $$x \neq 9$$

Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{x-4}$$?

Accepted Answer

$$x \geq 4$$

Question 2

Given $$f(x) = 3x^2$ + 5x - 12$$, what is the value of $$f(-4)$$?

Accepted Answer

$$-40$$

Question 3

For the function $$f(x) = \frac{5}{x-4}$$, which value of $$x is $$NOT in the domain?

Accepted Answer

$$x = 4$$

Question 4

If $$f(x) = 2x^2$ - 3x + 4$$, what is the difference quotient $$\frac{f(a+h) - f(a)}{h}$$?

Accepted Answer

$$4a h + 2h^2$ - 3h$$

Question 5

Which of the following is the correct interpretation of the net change of a function $$f$$ from $$x = a to$$ $$x = b$$?

Accepted Answer

$$f(b) - f(a)$$

Question 6

Given $$f(x) = \frac{\sqrt{x}}{x-9}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$x \u003e 0$$ and $$x 
eq 9$$

Question 7

For $$f(x) = 3x + 2$$, which of the following is the correct output when the input is $$x = 5$$?

Accepted Answer

$$17$$

Question 8

Suppose $$f(x) = 2x^2$ - 3x + 4. $$What is $$f(a) in $$terms of $$a$$?

Accepted Answer

$$2a^2 - 3a + 4$

Question 9

If $$f(x) = \frac{1}{x-4}$$, which value of $$x$$ makes $$f(x)$$ undefined?

Accepted Answer

$$x = 4$$

Question 10

Given $$f(x) = 3x^2$ + 5x - 12$$, what is the net change in $$f(x)$$ from $$x = -4 to$$ $$x = 3$$?

Accepted Answer

$$f(3) - f(-4) = 24 - (-40) = 64$$

Question 11

Which of the following best describes the independent variable in a function machine diagram?

Accepted Answer

The input value

Question 12

For $$f(x) = 2x^2$ - 3x + 4$$, what is $$f(a+h)$$?

Accepted Answer

$$2(a+h)^2 - 3(a+h) + 4$

Question 13

Which of the following is NOT a function?

Accepted Answer

A rule that assigns two outputs to a single input

Question 14

If $$f(x) = 3x^2$ + 5x - 12$$, what is $$f(\sqrt{7})$$?

Accepted Answer

$$3(\sqrt{7})^2$ + 5\sqrt{7} - 12$$

Question 15

Which of the following is the correct definition of the domain of a function?

Accepted Answer

The set of all values of $$x$$ for which $$f(x) is $$real

Question 16

For $$f(x) = 2x^2$ - 3x + 4$$, what is the value of $$f(0)$$?

Accepted Answer

$$4$$

Question 17

If $$f(x) = 3x^2$ + 5x - 12$$, what is $$f(-1)$$?

Accepted Answer

$$-10$$

Question 18

Which of the following functions has a domain of all real numbers except $$x = 4$$?

Accepted Answer

$$f(x) = \frac{1}{x-4}$$

Question 19

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

Accepted Answer

$$6$$

Functions: Definitions, Evaluation, Net Change, and Domain

Study Guide - Practice Questions