Question 1

Which of the following is the correct set-builder notation for the interval $$(-\infty, 2]$$?

Accepted Answer

$$\{x \mid x \leq 2\}$$

Question 2

Solve the rational equation $$\dfrac{2x}{x+2} + 3 = \dfrac{4}{x+2}$$ for $$x.$$

Accepted Answer

$$x = 2$$

Question 3

Which of the following quadratic equations can be solved by factoring and using the zero product property?

Accepted Answer

$$2x^2 - 3x - 4 = 0$

Question 4

Solve the inequality $$-5x - 3 \geq 7 - 4x.$$

Accepted Answer

$$x \leq -2$$

Question 5

What is the solution set for the polynomial inequality $$x^2 - 3x + 2$$ \geq 0$$?

Accepted Answer

$$(-\infty, 1] \cup [2, \infty)$$

Question 6

Given the relation $$\{(3,7), (-3,2), (-4,5), (1,4), (3,-4)\}$$, is this relation a function?

Accepted Answer

No, because the $$x-$$value $$3 is $$paired with two different $$y-$$values.

Question 7

Which of the following best describes a function?

Accepted Answer

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

Question 8

Given $$f(x) = x^2$ + x - 1$$, what is $$f(a-1)$$?

Accepted Answer

$$(a-1)^2 + (a-1) - 1$

Question 9

If $$f(x) = 2x^2$ - 5x - 3$$ and $$g(x) = \dfrac{1}{3}(x-2)^2$ - 6$$, what is $$g(2)$$?

Accepted Answer

$$-6$$

Question 10

Which of the following graphs passes the vertical line test and represents a function?

Accepted Answer

A graph where no vertical line intersects the graph more than once.

Question 11

Given $$f(x) = \dfrac{2x^2$ - 5x - 3}{3x - 1}$$, for which value of $$x is$$ $$f(x)$$ undefined?

Accepted Answer

$$x = \dfrac{1}{3}$$

Question 12

What is the domain of the function $$f(x) = \sqrt{x-4}$$?

Accepted Answer

$$[4, \infty)$$

Question 13

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

Accepted Answer

$$16$$

Question 14

Which of the following best describes the independent variable in a function?

Accepted Answer

The variable whose value determines the value of other variables.

Question 15

Given the function $$f(x) = x^2$ - 4x + 4$$, which of the following ordered pairs lies on its graph?

Accepted Answer

$$(2, 0)$$

Question 16

Which of the following intervals represents the solution to the inequality $$\dfrac{x}{x-4} \u003c 0$$?

Accepted Answer

$$(0, 4)$$

Question 17

If $$f(x) = x^2$ + x - 1$$, what is $$\dfrac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$2x + h + 1$$

Question 18

A pharmacist needs to ensure a medication's dosage, $$D$$, is a function of a patient's weight, $$w. $$Which statement is true?

Accepted Answer

For each weight $$w$$, there is exactly one dosage $$D$$ assigned.

Question 19

Given $$f(x) = 2x^2$ - 5x - 3$$, find all $$x$$ such that $$f(x) = 0.$$

Accepted Answer

$$x = 3,\ x = -\dfrac{1}{2}$$

College Algebra Study Notes: Equations, Inequalities, and Functions

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