Question 1

Which of the following is the correct equation of a circle with center at $$(2, -3)$$ and radius $$5$$?

Accepted Answer

$$ (x - 2)^2$ + (y + 3)^2$ = 25 $$

Question 2

Solve the inequality $$2x - 5 \u003e 7$$ and choose the correct solution set.

Accepted Answer

$$ x \u003e 6 $$

Question 3

Which of the following functions is the inverse of $$f(x) = 3x + 4$$?

Accepted Answer

$$ f$$^{-1}$$(x) = \frac{x - 4}{3} $$

Question 4

A population of bacteria doubles every 4 hours. If the initial population is 500, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$ P = 500 \cdot 2$$^{t/4}$$ $$

Question 5

Which of the following is the solution to the system of equations: $$\begin{cases} x + y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$ x = 4,\ y = 3 $$

Question 6

Which of the following best describes the graph of $$y = \frac{1}{x}$$?

Accepted Answer

It has two branches, one in Quadrant I and one in Quadrant III, and both approach the axes but never touch them.

Question 7

If $$f(x) = x^2$ - 4x + 7$$, what is the vertex of the parabola?

Accepted Answer

$$ (2, 3) $$

Question 8

Which of the following is equivalent to $$\log_2$(32)$$?

Accepted Answer

$$ 5 $$

Question 9

A chemical reaction follows the equation $$C = C_0$ e$$^{-kt}$$, where C_0$ is the initial concentration, k$ is a positive constant, and t$ is time. If C_0$ = 100$$ and $$k = 0.2$$, what is $$C$$ after $$5$$ units of time?

Accepted Answer

$$ 100 e$$^{-1}$$ $$

Question 10

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

Accepted Answer

$$ x = 3  or$$ $$ x = -\frac{5}{3} $$

Question 11

Which of the following is the domain of the function $$f(x) = \sqrt{x - 5}$$?

Accepted Answer

$$ [5, \infty) $$

Question 12

If $$f(x) = 2x + 1$$ and $$g(x) = x^2$, what is (f$$ \circ g)(3)$$?

Accepted Answer

$$ 19 $$

Question 13

Which of the following lines is perpendicular to the line $$y = -\frac{1}{2}x + 3$$?

Accepted Answer

$$ y = 2x - 1 $$

Question 14

A car's value depreciates exponentially according to $$V = 20000 \cdot (0.85)^t$$, where $$t is $$the number of years after purchase. What is the value after $$3$$ years?

Accepted Answer

$$ 20000 \cdot (0.85)^3$ $$

Question 15

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

Accepted Answer

$$ x = 4 $$

Question 16

If $$f(x) = \frac{1}{x-2}$$, which of the following statements is true?

Accepted Answer

The function is undefined at $$x = 2.$$

Question 17

Which of the following is the correct solution to the equation $$\log_{3}(x) = 2$$?

Accepted Answer

$$ x = 9 $$

Question 18

A student’s quiz average is calculated by dropping the lowest of 13 quiz scores. If the scores are $$[80, 85, 90, 70, 95, 100, 88, 92, 84, 78, 91, 87, 93]$$, what is the average used for the course grade?

Accepted Answer

$$ 89.5 $$

Question 19

Which of the following best describes the range of the function $$f(x) = e^x$$?

Accepted Answer

$$ (0, \infty) $$

Math 1021 College Algebra Syllabus and Course Structure Overview

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