Question 1

Which of the following is the correct slope-intercept form of the line given by $$4x + 2y = 8$$?

Accepted Answer

$$y = -2x + 4$$

Question 2

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

Accepted Answer

$$(-\infty, 6) \cup (6, \infty)$$

Question 3

Given the function $$f(x) = x^2$ - 2x + 5$$, what is $$f(-2)$$?

Accepted Answer

$$13$$

Question 4

A company had 20 customers at month 1 and 50 customers at month 4. What is the average rate of change in customers per month?

Accepted Answer

$$10$$

Question 5

Find the slope of the line passing through the points $$(1,3)$$ and $$(5,11).$$

Accepted Answer

$$2$$

Question 6

Which of the following is the equation of the line with slope $$2$$ passing through the point $$(3,4)$$?

Accepted Answer

$$y = 2x - 2$$

Question 7

What is the slope of a line perpendicular to the line $$y = -4x + 7$$?

Accepted Answer

$$\dfrac{1}{4}$$

Question 8

Solve the inequality $$-3x + 2 \geq 14$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, -4]$$

Question 9

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

Accepted Answer

$$[4, \infty)$$

Question 10

A piecewise function is defined as $$f(x) = 3x - 1$$ for $$x \u003c 2$$ and $$f(x) = x + 5$$ for $$x \geq 2. $$What is $$f(2)$$?

Accepted Answer

$$7$$

Question 11

Which of the following points is a solution to the equation $$x^2 + y = 7$?

Accepted Answer

$$(2,3)$$

Question 12

If $$f(x) = \dfrac{\sqrt{x+3}}{7(x-1)}$$, what is the domain of $$f$$?

Accepted Answer

$$[-3,1) \cup (1, \infty)$$

Question 13

Which of the following lines is parallel to the line $$y = \dfrac{3}{2}x - 5$$?

Accepted Answer

$$y = \dfrac{3}{2}x + 1$$

Question 14

Given the function $$f(x) = x^2$ + 3x - 4$$, what is $$f(a+5)$$?

Accepted Answer

$$a^2 + 13a + 36$

Question 15

A taxi company charges a flat fee of $$\3$ plus $$\$$2$$ per mile. Which equation models the total cost $$C$$ for $$m$$ miles?

Accepted Answer

$$C = 2m + 3$$

Question 16

Which of the following intervals represents all $$x-$$values where the graph of a function is increasing?

Accepted Answer

$$(a, b)$$ where the graph rises from left to right between $$x = a$$ and $$x = b$$

Question 17

If a line has a slope of $$-3$$, what is the slope of a line perpendicular to it?

Accepted Answer

$$\dfrac{1}{3}$$

Question 18

Solve for $$y in $$the equation $$x = 2y + 1.$$

Accepted Answer

$$y = \dfrac{1}{2}x - \dfrac{1}{2}$$

Question 19

Which of the following best describes the effect of multiplying both sides of an inequality by a negative number?

Accepted Answer

The inequality sign must be flipped.

Question 20

Given the piecewise function $$f(x) = \begin{cases} x+2 & x \u003c 1 \ 3 & x \geq 1 \end{cases}$$, what is the value of $$f(1)$$?

Accepted Answer

$$3$$

College Algebra Study Guide: Lines, Functions, Domains, Inequalities, and Piecewise Functions

Study Guide - Practice Questions