Question 1

Which of the following intervals represents the solution set to the inequality $$x^3$$ - $$3x^2 + 2x$$ \geq 0$$?

Accepted Answer

$$[0,1] \cup [2, \infty)$$

Question 2

Given the equation $$\frac{2x}{x-2} + 3 = \frac{4}{x-2}$$, what is the solution set?

Accepted Answer

No solution

Question 3

Which of the following is the correct set-builder notation for the interval $$(-\infty, 1) \cup (4, \infty)$$?

Accepted Answer

$$\{x \mid x  4\}$$

Question 4

Which of the following relations is NOT a function?

Accepted Answer

$$\{(1,2), (1,3), (2,4)\}$$

Question 5

What is the domain of the function $$f(x) = \frac{1}{x+1}$$?

Accepted Answer

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

Question 6

Given the quadratic equation $$6x^2 - 17x + 12 = 0$, what are its solutions?

Accepted Answer

$$x = \frac{3}{2}, \frac{4}{3}$$

Question 7

Which of the following best describes a function?

Accepted Answer

A relation where each element in the domain is paired with exactly one element in the range.

Question 8

If $$y = x^2$ - 4x + 4$$, what is the vertex of the parabola?

Accepted Answer

$$(2, 0)$$

Question 9

Which of the following describes the range of the function $$f(x) = x^2$ - 4x + 4$$?

Accepted Answer

$$[0, \infty)$$

Question 10

Given the relation $$\{(0,7), (1,5), (2,7), (3,6)\}$$, what is the domain?

Accepted Answer

$$\{0,1,2,3\}$$

Question 11

Which of the following equations does NOT represent $$y as a $$function of $$x$$?

Accepted Answer

$$x^2$$ + $$y^2 = 16$

Question 12

What is the solution set to the inequality $$x-4 \u003c 0$$?

Accepted Answer

$$(-\infty, 4)$$

Question 13

If $$f(x) = \frac{1}{x-2}$$, which value is NOT in the domain of $$f$$?

Accepted Answer

$$x = 2$$

Question 14

Which of the following best describes the range of the relation $$\{(a, e), (b, f), (c, g), (d, f)\}$$?

Accepted Answer

$$\{e, f, g\}$$

Question 15

Which of the following is the correct interval notation for the set $$\{x \mid x \leq -1 	ext{ or } x \u003e 4\}$$?

Accepted Answer

$$(-\infty, -1] \cup (4, \infty)$$

Question 16

If $$f(x) = x^2$ - 4x + 4$$, what is $$f(3)$$?

Accepted Answer

$$1$$

Question 17

Which of the following is the correct definition of a relation?

Accepted Answer

A correspondence between two sets such that each element of the first set is paired with one or more elements of the second set.

Question 18

Given the function $$f(x) = \frac{1}{x^2$ - 9}$$, what is the domain?

Accepted Answer

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

Question 19

If a relation has domain $$\{a, b, c, d\}$$ and range $$\{e, f, g\}$$, which of the following could be a function?

Accepted Answer

$$\{(a,e), (b,f), (c,g), (d,f)\}$$

Foundations of Relations, Functions, and Equations in College Algebra

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