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

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 $\dfrac{x}{x-4} < 0$?

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

Study Guide - Practice Questions