Question 1

Given the relation $$\{(-2, 4), (5, 5), (-6, 8), (7, 5), (-10, -10), (7, -1)\}$$, what is the domain and range of the relation? Is it a function?

Accepted Answer

Domain: $$\{-10, -6, -2, 5, 7\}$$, Range: $$\{-10, -1, 4, 5, 8\}$$, Not a function

Question 2

For the function $$f(x) = x + 4$$, what is $$f(2x + 2)$$?

Accepted Answer

$$2x + 6$$

Question 3

Find the difference quotient for $$f(x) = x^2$ + 5x - 7.$$

Accepted Answer

$$2x + h + 5$$

Question 4

Given $$f(x) = \dfrac{5}{x^2$ + 6}$$, what is the difference quotient $$\dfrac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$\dfrac{\dfrac{5}{(x+h)^2$ + 6} - \dfrac{5}{x^2$ + 6}}{h}$$

Question 5

What is the domain of the function $$f(x) = \dfrac{1}{x^2$ - x - 6}$$?

Accepted Answer

$$(-\infty, -2) \cup (-2, 3) \cup (3, \infty)$$

Question 6

Given $$f(x) = x^2$ - 1$$, what is the range of $$f(x)$$?

Accepted Answer

$$[-1, \infty)$$

Question 7

Determine if the function $$f(x) = 4x^2$ + 2x is $$even, odd, or neither.

Accepted Answer

Neither

Question 8

Which parent function best models the height of a ball thrown upward from the ground over time?

Accepted Answer

$$f(x) = x^2$ (Quadratic function)

Question 9

Given the piecewise function $$f(x) = \begin{cases} 4, & x \leq -2 \ x-2, & -2 \u003c x \u003c 2 \ -2x+4, & x \geq 2 \end{cases}$$, what is $$f(3)$$?

Accepted Answer

$$-2$$

Question 10

Find the average rate of change of $$f(x) = 3x^2$ + 7x - 2$$ over the interval $$[-1, 3].$$

Accepted Answer

$$10$$

Question 11

Which of the following is the correct domain for $$f(x) = \dfrac{1}{x+2}$$?

Accepted Answer

$$(-\infty, -2) \cup (-2, \infty)$$

Question 12

Given $$f(x) = |x|$$, which statement is true about its symmetry?

Accepted Answer

It is even and symmetric about the y-axis.

Question 13

Which of the following is the range of $$f(x) = \sin(x)$$?

Accepted Answer

$$[-1, 1]$$

Question 14

If $$f(x) = x^3$, which of the following statements is true?

Accepted Answer

The function is odd and symmetric about the origin.

Question 15

Given $$f(x) = \dfrac{1}{x^2$ - 25}$$, what is the domain?

Accepted Answer

$$(-\infty, -5) \cup (-5, 5) \cup (5, \infty)$$

Question 16

Which of the following is the correct range for $$f(x) = \dfrac{1}{x}$$?

Accepted Answer

$$(-\infty, 0) \cup (0, \infty)$$

Precalculus Review: Functions, Domain & Range, Symmetry, and Parent Functions

Study Guide - Practice Questions