Question 1

Which of the following equations is NOT linear?

Accepted Answer

$$y = x^2$ + 4$$

Question 2

Solve the equation for $$x$$: $$\frac{2x}{3} - \frac{5}{6} = \frac{1}{2}$$

Accepted Answer

$$x = 2$$

Question 3

Which of the following sets of ordered pairs represents a function?

Accepted Answer

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

Question 4

Solve the inequality and write the solution in interval notation: $$\frac{x}{2} - 3 \u003c 1$$

Accepted Answer

$$(-\infty, 8)$$

Question 5

Which of the following equations has no solution?

Accepted Answer

$$3x - 5 = 3x + 2$$

Question 6

Given the function $$f(x) = 2x^2$ - 3x + 1$$, what is $$f(-2)$$?

Accepted Answer

$$f(-2) = 15$$

Question 7

Which of the following graphs represents a nonlinear equation?

Accepted Answer

A parabola

Question 8

Solve for $$y in $$terms of $$x$$: $$3y - 2x = 12$$

Accepted Answer

$$y = \frac{2x + 12}{3}$$

Question 9

A medical researcher is tracking the temperature $$T (in$$ $$^\circC) of a $$patient over time $$t (in $$hours) using the function $$T(t) = 37 - 0.5t. $$What is the patient's temperature after 4 hours?

Accepted Answer

$$T(4) = 35^\circC$$

Question 10

Solve the compound inequality: $$-3 \u003c 2x - 1 \leq 5$$

Accepted Answer

$$(-1, 3]$$

Question 11

Which of the following best describes the domain of the function $$f(x) = \frac{1}{x-2}$$?

Accepted Answer

$$(-\infty, 2) \cup (2, \infty)$$

Question 12

A chemical reaction's rate $$R (in $$mol/L/s) is modeled by $$R(t) = 5t + 2. If $$the reaction starts at $$t=0$$, what is the rate after 6 seconds?

Accepted Answer

$$R(6) = 32$$ mol/L/s

Question 13

Which of the following inequalities has all real numbers as its solution?

Accepted Answer

$$2x + 3 \u003c 2x + 5$$

Question 14

Given the set of ordered pairs $$\{(1,2), (2,3), (3,4), (2,5)\}$$, is this set a function?

Accepted Answer

No, because the input 2 is paired with two different outputs.

Question 15

Solve the inequality: $$\frac{3x - 2}{4} \geq 1$$

Accepted Answer

$$[2, \infty)$$

Question 16

A car rental company charges a base fee of $$\20$ plus $$\$$0.15$$ per mile driven. Which equation models the total cost $$C$$ for $$m$$ miles driven?

Accepted Answer

$$C = 20 + 0.15m$$

Question 17

Which of the following is the range of the function $$f(x) = x^2$ for x$ in $$[-2, 3]$$?

Accepted Answer

$$[0, 9]$$

Question 18

Solve for $$x$$: $$\frac{5x + 2}{3} = \frac{2x - 1}{2}$$

Accepted Answer

$$x = 4$$

Question 19

A biologist models the population $$P of a $$bacteria culture after $$t$$ hours as $$P(t) = 1000 + 50t. $$What is the population after 8 hours?

Accepted Answer

$$P(8) = 1400$$

Intermediate Algebra: Equations, Inequalities, and Introduction to Functions – Test Study Guide

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