Question 1

Which of the following numbers is an irrational number?

Accepted Answer

$$\sqrt{2}$$

Question 2

Evaluate the expression $$3x - y$$ for $$x = 10$$ and $$y = 6.$$

Accepted Answer

$$24$$

Question 3

For which values of $$y is $$the rational expression $$\frac{y+4}{y^2$-16}$$ undefined?

Accepted Answer

$$y = 4, -4$$

Question 4

Find all numbers that must be excluded from the domain of $$\frac{x-3}{x^2$+9x+8}.$$

Accepted Answer

$$x = -1, -8$$

Question 5

Simplify the rational expression $$\frac{3x-9}{x^2$-6x+9}$$ and state the value(s) that must be excluded from the domain.

Accepted Answer

Simplified: $$\frac{3}{x-3}$$; Exclude $$x = 3$$

Question 6

Which of the following is the correct simplification of $$\frac{x^2$-12x+36}{4x-24}$$ and the value(s) to be excluded from the domain?

Accepted Answer

Simplified: $$\frac{x-6}{4}$$; Exclude $$x = 6$$

Question 7

Given the rational expression $$\frac{y^2$-3y-54}{y^2$-4y-45}$$, what is its simplified form and which values must be excluded from the domain?

Accepted Answer

Simplified: $$\frac{y+6}{y+5}$$; Exclude $$y = 9, -5$$

Question 8

Evaluate the expression $$x^2 + 6x$ for x = 2$.

Accepted Answer

$$16$$

Question 9

Which of the following points is located in Quadrant II of the rectangular coordinate system?

Accepted Answer

$$(-3, 5)$$

Question 10

What is the $$x-$$intercept of the graph of $$y = 4 - x^2$?

Accepted Answer

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

Question 11

Which of the following best describes the set of all numbers that can be written as a ratio of two integers?

Accepted Answer

Rational numbers

Question 12

Which of the following expressions is undefined for $$x = 4$$?

Accepted Answer

$$\frac{x+4}{x-4}$$

Question 13

If $$A = (2, -3)$$, $$B = (2, 4)$$, and $$C = (0, 0)$$, which point lies on the $$y-$$axis?

Accepted Answer

$$C$$

Question 14

Which of the following is a solution to the equation $$y = 4 - x^2$?

Accepted Answer

$$(2, 0)$$

Question 15

Which of the following best describes the $$y-$$intercept of a graph?

Accepted Answer

The $$y-$$coordinate where the graph crosses the $$y-$$axis

College Algebra Study Guidance: Rational Expressions, Algebraic Evaluation, and Graphs

Study Guide - Practice Questions