Question 1

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

Accepted Answer

A relation where each input is paired with exactly one output.

Question 2

Given the function $$f(x) = 2x^2$ - 8x + 6$$, what are the coordinates of its vertex?

Accepted Answer

$$(2, -2)$$

Question 3

Which of the following is the correct simplification of $$\sqrt{50} + 2\sqrt{8}$$?

Accepted Answer

$$7\sqrt{2}$$

Question 4

Solve the equation $$|2x - 5| = 9.$$

Accepted Answer

$$x = 7,\ x = -2$$

Question 5

Which of the following is the correct inverse of the function $$f(x) = 3x + 7$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 7}{3}$$

Question 6

A population of bacteria doubles every 3 hours. If the initial population is 200, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P = 200 \cdot 2$$^{t/3}$$

Question 7

Which of the following is the correct solution to the equation $$x^2 + 4x + 13 = 0$?

Accepted Answer

$$x = -2 \pm 3i$$

Question 8

Given $$f(x) = x^2$ and g(x) = x + 1$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$9$$

Question 9

Which of the following describes the transformation of the graph of $$y = x^2$ to y = (x$$ - $$3)^2 + 2$?

Accepted Answer

Shift right 3 units and up 2 units

Question 10

Which of the following is the correct domain of the function $$f(x) = \frac{1}{x^2$ - 9}$$?

Accepted Answer

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

Question 11

A chemical reaction follows the equation $$A(t) = 100e$$^{-0.05t}$$, where A(t$$)$$ is the amount of substance left after t$ minutes. How much substance remains after 20 minutes (rounded to the nearest whole number)?

Accepted Answer

Question 12

Which of the following is the correct solution to the equation $$\log_2$(x - 1) = 3$$?

Accepted Answer

$$x = 9$$

Question 13

If $$f(x) = \frac{x^2$ - 4}{x - 2}$$, what is the simplified form of $$f(x)$$ for $$x 
eq 2$$?

Accepted Answer

$$x + 2$$

Question 14

Which of the following is the correct solution to the radical equation $$\sqrt{x + 3} = x - 1$$?

Accepted Answer

$$x = 2$$

Question 15

Which of the following is the correct application of the properties of logarithms to simplify $$\log_3$(27x)$$?

Accepted Answer

$$3 + \log_3$(x)$$

Question 16

A rational function has a vertical asymptote at $$x = 4. $$Which of the following could be its equation?

Accepted Answer

$$f(x) = \frac{2x}{x - 4}$$

Question 17

Which of the following is the correct solution to the inequality $$|3x - 2| \u003c 7$$?

Accepted Answer

$$-\frac{5}{3} \u003c x \u003c 3$$

Question 18

Given $$f(x) = x^3$ - 6x^2$ + 11x - 6$$, which of the following is NOT a zero of $$f(x)$$?

Accepted Answer

$$x = 4$$

Question 19

If $$f(x) = 2x + 1$$ and $$g(x) = x^2$, what is the difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$2$$

Question 20

Which of the following is the correct solution to the equation $$2^{x+1} = 16$?

Accepted Answer

$$x = 3$$

College Algebra & Trigonometry Syllabus and Course Structure Study Guide

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