$$x \in \mathbb{R}, x \neq 3, x \neq -2$$

$$x \in \mathbb{R}, x \neq -1$$

Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{4x-1}$$?

Accepted Answer

$$x \in [\frac{1}{4}, \infty)$$

Question 2

Given the function $$f(x) = 2x^2$ + x - 15$$, what are the $$x-$$intercepts?

Accepted Answer

$$x = 5$$ and $$x = -3$$

Question 3

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$

Question 4

A function $$f is $$said to be odd if:

Accepted Answer

$$f(-x) = -f(x)$$ for all x$

Question 5

What is the range of the function $$f(x) = \sqrt{x-1}$$?

Accepted Answer

$$y \in [0, \infty)$$

Question 6

Which of the following is the correct domain for the function $$f(x) = \frac{1}{x-3}$$?

Accepted Answer

$$x \in \mathbb{R}, x 
eq 3$$

Question 7

If a graph is symmetric with respect to the y-axis, which of the following must be true?

Accepted Answer

For every $$(x, y)$$, $$(-x, y) is $$also on the graph.

Question 8

Given $$f(x) = x^2$ - 2x + 1$$, what is the difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$2x + h - 2$$

Question 9

Which of the following intervals describes where the function $$f(x) is $$increasing if $$f(x)$$ has a minimum at $$x = -1$$ and $$x = 3$$?

Accepted Answer

$$x \in (-1, 3)$$

Question 10

For the function $$f(x) = \frac{1}{x-3} + \frac{1}{x+2}$$, what is the domain?

Accepted Answer

$$x \in \mathbb{R}, x 
eq 3, x 
eq -2$$

Question 11

If $$f(x) = x^2$ and g(x) = x+1$, what is the domain of $$\frac{f(x)}{g(x)}$$?

Accepted Answer

$$x \in \mathbb{R}, x 
eq -1$$

Question 12

Which of the following is NOT a property of an even function?

Accepted Answer

Its graph is symmetric with respect to the origin.

Question 13

Given the function $$f(x) = x^2$ - 4$$, what are the $$x-$$intercepts?

Accepted Answer

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

Question 14

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

Accepted Answer

$$y \in [2, \infty)$$

Question 15

If $$f(x) = x^2$ and g(x) = x-3$, what is the domain of $$\frac{f(x)}{g(x)}$$?

Accepted Answer

$$x \in \mathbb{R}, x 
eq 3$$

Question 16

Which of the following is true about the symmetry of the graph of $$y = x^2$?

Accepted Answer

It is symmetric with respect to the y-axis.

Question 17

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

Accepted Answer

$$f(x) is an $$odd function.

Question 18

Given $$f(x) = x^2$ - 2x + 1$$, what is the value of the difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$2x + h - 2$$

Question 19

Which of the following is the correct interval notation for the set $$x \in \mathbb{R}, x 
eq 3, x 
eq -2$$?

Accepted Answer

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

Functions and Their Graphs: Intercepts, Symmetry, Domain, Range, and Operations

Study Guide - Practice Questions