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

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

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

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

Q: If $$f(x) = x^2$ - 4$$ and $$g(x) = x + 2$$, what is the domain of $$\frac{f(x)}{g(x)}$$?

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

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

$$(5, 0)$$ and (-3, 0)$

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 $$f(x) = x^2$ + 2$$?

Accepted Answer

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

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

Accepted Answer

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

Question 8

Which of the following statements is true about the symmetry of the function $$f(x) = x^4$?

Accepted Answer

It is symmetric about the y-axis.

Question 9

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

Accepted Answer

$$(2, 0)$$ and $$(-2, 0)$$

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

A function is said to be increasing on an interval if:

Accepted Answer

$$f(x_1$) \u003c f(x_2$)$$ whenever $$x_1$$ \u003c $$x_2 in $$the interval

Question 12

Which of the following is the correct difference quotient for $$f(x) = x^2$?

Accepted Answer

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

Question 13

If $$f(x) = x^2$ - 4$$ and $$g(x) = x + 2$$, what is the domain of $$\frac{f(x)}{g(x)}$$?

Accepted Answer

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

Question 14

Which of the following is NOT a property of even functions?

Accepted Answer

Their graphs are symmetric about the origin.

Question 15

Given the function $$f(x) = x^3$ - x$$, determine if it is even, odd, or neither.

Accepted Answer

Odd

Question 16

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

Accepted Answer

$$x \in (-4, 0)$$

Question 17

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

Accepted Answer

$$2x + h + 2$$

Question 18

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

Accepted Answer

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

Question 19

Given $$f(x) = x^2$ - 4$$ and $$g(x) = x + 2$$, what is $$(f+g)(x)$$?

Accepted Answer

$$x^2 + x - 2$

Functions, Graphs, and Their Properties: Precalculus Study Guide

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