Question 1

Which of the following values is NOT in the domain of the function $$f(x) = \frac{2}{x+3} - \frac{1}{x-2}$$?

Accepted Answer

$$x = -3$$

Question 2

Given the equation $$\frac{4}{x+10} + \frac{1}{x+2} = \frac{5x+1}{(x+10)(x+2)}$$, what is the equation after clearing the denominators?

Accepted Answer

$$4(x+2) + 1(x+10) = 5x+1$$

Question 3

Solve for $$x$$: $$8x\left(\frac{2}{x}\right) + 8x(1) = \frac{3x}{4x} + 8x\left(\frac{15}{8x}\right).$$

Accepted Answer

$$x = \frac{10}{7}$$

Question 4

What values make the denominator zero in the rational expression $$\frac{6x}{x+2}$$?

Accepted Answer

$$x = -2$$

Question 5

Solve for $$x$$: $$4x = 3x + 4 - \frac{4}{x+2}.$$

Accepted Answer

$$x = \frac{2}{3}$$

Question 6

Which of the following is the solution set for $$x^2 - 6x - 10 = 0$?

Accepted Answer

$$x = 3 + \sqrt{19}, x = 3 - \sqrt{19}$$

Question 7

Express the solution to $$-6x \leq 18 in $$interval notation.

Accepted Answer

$$[-3, \infty)$$

Question 8

Solve the absolute value inequality $$|2x-1| \u003c 3$$ and express the solution in interval notation.

Accepted Answer

$$(-1, 2)$$

Question 9

Solve the absolute value equation $$|5x-2| = 13.$$

Accepted Answer

$$x = 3, x = -\frac{11}{5}$$

Question 10

Given the relation $$\{(3,2), (4,-1), (5,5)\}$$, determine if it is a function and state the domain.

Accepted Answer

It is a function; domain is $$\{3,4,5\}$$

Question 11

Use the vertical line test to determine if $$y is a $$function of $$x$$ for a circle centered at the origin.

Accepted Answer

No, $$y is $$not a function of $$x.$$

Question 12

Given the function $$f(x)$$ with domain $$(-\infty, \infty)$$ and range $$[1, \infty)$$, which of the following statements is true?

Accepted Answer

The graph never goes below $$y=1.$$

Question 13

If $$f(x) = 2x + 5$$, what is $$f(3)$$?

Accepted Answer

$$11$$

Question 14

Which interval notation represents all real numbers $$x$$ such that $$x \geq 7$$?

Accepted Answer

$$[7, \infty)$$

Question 15

Solve the inequality $$-8 + 2x - 2x \leq 8$$ and express the solution in interval notation.

Accepted Answer

$$[0, 8]$$

Question 16

Given the relation $$\{(-2,3), (3,-1), (-2,2), (3,4)\}$$, is it a function?

Accepted Answer

No, because $$-2$$ repeats in the domain.

Question 17

If $$f(x) = x^2$ - 7x - 10$$, what are the zeros of the function?

Accepted Answer

$$x = -5, x = 2$$

Question 18

Solve the absolute value inequality $$|x-4| \geq 6$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, -2] \cup [10, \infty)$$

Question 19

Given $$f(x) = x^2$ - 11x + 10$$, what are the solutions to $$f(x) = 0$$?

Accepted Answer

$$x = 10, x = 1$$

College Algebra Study Guide: Rational Equations, Functions, and Inequalities

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