Q: Given $$f(x) = \frac{1}{x-3}$$ and $$g(x) = \frac{1}{x+2}$$, what is the domain of $$(f+g)(x)$$?

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

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

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

Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

$$(3,0), (-2.5, 0)$$

Question 3

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$

Question 4

A function $$f is $$said to have origin symmetry if:

Accepted Answer

$$f(-x) = -f(x)$$

Question 5

Given $$f(x) = \sqrt{4x-1}$$, what is the domain of $$f$$?

Accepted Answer

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

Question 6

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 7

If $$f(x) = x^2$ - 4$$, for which values of $$x is$$ $$f(x) = 0$$?

Accepted Answer

$$x = 2 or$$ $$x = -2$$

Question 8

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

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

Question 9

Given $$f(x) = \frac{1}{x-3}$$ and $$g(x) = \frac{1}{x+2}$$, what is the domain of $$(f+g)(x)$$?

Accepted Answer

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

Question 10

Which of the following best describes the symmetry of the function $$f(x) = x^3$?

Accepted Answer

Odd symmetry (origin)

Question 11

If a function is reflected over the y-axis, what happens to the coordinates of each point $$(x, y)$$?

Accepted Answer

They become $$(-x, y)$$

Question 12

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

Accepted Answer

$$2x + h + 2$$

Question 13

Which of the following is the correct range for $$f(x) = \sqrt{4 - x^2$}$$?

Accepted Answer

$$y \in [0, 2]$$

Question 14

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 15

Which of the following is NOT a valid method to test for y-axis symmetry?

Accepted Answer

Replace $$y$$ with $$-y$$ and check if the equation is unchanged

Question 16

Given the piecewise function representing shipping costs, what is the range if the minimum cost is $$10 and the maximum is 50$$?

Accepted Answer

$$[10, 50]$$

Question 17

If $$f(x) = x^2$ - 4x + 3$$, for which values of $$x$$ does $$f(x) = 0$$?

Accepted Answer

$$x = 1 or$$ $$x = 3$$

Question 18

Which of the following is the correct interval notation for $$x \in \mathbb{R}$$ except $$x = 3$$ and $$x = -2$$?

Accepted Answer

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

Question 19

If $$f(x) = x^2$ and g(x$$) = $$x^3$$, what is the domain of $$f(x) + g(x)$$?

Accepted Answer

$$x \in \mathbb{R}$$

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

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