Question 1

Which of the following is the correct definition of the domain of a function $$f(x)$$?

Accepted Answer

The set of all $$x$$ values for which $$f(x) is $$defined.

Question 2

A chemical reaction's temperature $$T (in $$degrees Celsius) is modeled by $$T(t) = 5t + 20$$, where $$t is $$time in minutes. What is the temperature after 8 minutes?

Accepted Answer

$$T(8) = 60$$

Question 3

Which of the following graphs represents a function?

Accepted Answer

A graph where every $$x$$ value corresponds to exactly one $$y$$ value.

Question 4

Given the equation $$y = 2x - 3$$, what is the $$y-$$intercept?

Accepted Answer

$$-3$$

Question 5

A hospital records the number of patients $$P as a $$function of time $$t in $$hours: $$P(t) = 12t + 5. $$How many patients are there after 4 hours?

Accepted Answer

$$P(4) = 29$$

Question 6

Which of the following is the solution set for $$2x + 5 = 13$$?

Accepted Answer

$$x = 4$$

Question 7

If $$f(x) = x^2$ - 4x + 7$$, what is $$f(3)$$?

Accepted Answer

$$f(3) = 10$$

Question 8

Which of the following is the correct solution to the system of equations: $$\begin{cases} x + y = 5 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$x = 3, y = 2$$

Question 9

A car rental company charges a flat fee of $$\25$ plus $$\$$0.20$$ per mile driven. Which equation models the total cost $$C$$ for $$m$$ miles?

Accepted Answer

$$C = 25 + 0.20m$$

Question 10

Which of the following is the correct factorization of $$x^2 - 9$?

Accepted Answer

$$(x - 3)(x + 3)$$

Question 11

If $$g(x) = 2x^2$ - 5x + 1$$, what is the vertex of the parabola?

Accepted Answer

$$(1.25, -2.125)$$

Question 12

Which of the following is the solution to $$\sqrt{x} = 5$$?

Accepted Answer

$$x = 25$$

Question 13

A population of bacteria doubles every hour. If the initial population is $$P_0 = 100$, what is the population after 3 hours?

Accepted Answer

$$P = 800$$

Question 14

Which of the following is the correct solution to $$|x - 4| = 7$$?

Accepted Answer

$$x = 11 or$$ $$x = -3$$

Question 15

A medication's concentration $$C in $$the bloodstream decreases exponentially: $$C(t) = 50e$$^{-0.2t}$$, where t$ is in hours. What is the concentration after 5 hours? (Round to the nearest whole number.)

Accepted Answer

$$C(5) \approx 18$$

Question 16

Which of the following is the correct solution to $$x^2 + 6x + 9 = 0$?

Accepted Answer

$$x = -3$$

Question 17

A business's profit $$P is $$given by $$P(x) = -2x^2$ + 40x - 100$$, where $$x is $$the number of units sold. What is the maximum profit?

Accepted Answer

$$P = 300$$

Question 18

Which of the following is the correct solution to $$3(x - 2) = 2x + 5$$?

Accepted Answer

$$x = 7$$

Question 19

If $$h(x) = \frac{1}{x}$$, which value of $$x is $$not in the domain of $$h(x)$$?

Accepted Answer

$$x = 0$$

College Algebra: Functions, Graphs, and Equations Study Guide

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