Question 1

Given the linear equation $$5x = 35$$, what are the x- and y-intercepts?

Accepted Answer

x-intercept: $$(7, 0)$$; y-intercept: none

Question 2

Find the slope of the line passing through the points $$(-4, 6)$$ and $$(8, 5).$$

Accepted Answer

$$m = -\frac{1}{12}$$

Question 3

What is the slope of the line $$2x + 5y = 35$$?

Accepted Answer

$$m = -\frac{2}{5}$$

Question 4

Find the domain of $$f(x) = \frac{x^2$ - 9}{x^2$ - 9} in $$interval notation.

Accepted Answer

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

Question 5

Given $$f(x) = \sqrt{3x - 4}$$, what is the domain of $$f$$?

Accepted Answer

$$\left[\frac{4}{3}, \infty\right)$$

Question 6

Find the equation of the line in slope-intercept form passing through $$(2, -2)$$ and $$(5, 4).$$

Accepted Answer

$$y = 2x - 6$$

Question 7

Evaluate the piecewise function $$f(x) = \begin{cases} 4x^2$ - 1 & x \leq 1 \ 3x - 7 & x \u003e 1 \end{cases} at$$ $$x = 3.$$

Accepted Answer

$$2$$

Question 8

Given $$f(x) = x^2$ - 10x + 16$$, what are the x-intercepts?

Accepted Answer

$$(8, 0)$$ and $$(2, 0)$$

Question 9

Find the inverse of $$f(x) = \frac{2x - 1}{x + 3}.$$

Accepted Answer

$$f^{-1}(x$$) = \frac{3x + 1}{2 - x}$$

Question 10

Given $$f(x) = x^2$ - 4x$$ and $$g(x) = 3x - 2$$, evaluate $$(f + g)(-3).$$

Accepted Answer

$$10$$

Question 11

For the function $$f(x) = -4(x - 4)^2$ + 36$$, what is the vertex?

Accepted Answer

$$(4, 36)$$

Question 12

Is the graph of the function shown in $$image_1 a $$function?

Accepted Answer

Yes

Question 13

Given $$f(x) = x^2$ - 3x + 7$$, find and simplify $$\frac{f(x + h) - f(x)}{h}.$$

Accepted Answer

$$2x + h - 3$$

Question 14

What is the domain of $$g(x) = \sqrt{2 - x}$$?

Accepted Answer

$$(-\infty, 2]$$

Question 15

Given $$f(x) = x^2$ - 4x$$ and $$g(x) = 3x - 2$$, evaluate $$(fg)(-2).$$

Accepted Answer

$$-96$$

Question 16

Find the y-intercept of $$f(x) = x^2$ - 10x + 16.$$

Accepted Answer

$$(0, 16)$$

Question 17

Given $$f(x) = 2x^2$ + 3$$, find and simplify $$\frac{f(x + h) - f(x)}{h}.$$

Accepted Answer

$$4x + 2h$$

Question 18

Which of the following is the correct inverse for $$f(x) = 3 + \sqrt{x + 7}$$?

Accepted Answer

$$f^{-1}(x) = (x$$ - $$3)^2 - 7$

Question 19

Given $$f(x) = x^2$ - 10x + 16$$, what is the vertex?

Accepted Answer

$$(5, -9)$$

Question 20

Given $$f(x) = x^2$ - 4x$$ and $$g(x) = 3x - 2$$, evaluate $$(f - g)(5).$$

Accepted Answer

$$-8$$

Precalculus Review: Intercepts, Slope, Domain, Functions, and Quadratics

Study Guide - Practice Questions