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

Solve the following linear equation for $$x$$: $$3x - 7 = 2x + 5.$$

Accepted Answer

$$x = 12$$

Question 3

Which of the following is the graph of a quadratic function?

Accepted Answer

A parabola

Question 4

Given the function $$f(x) = 2x^2$ - 4x + 1$$, what is the vertex of the parabola?

Accepted Answer

$$(1, -1)$$

Question 5

Which of the following equations represents an exponential function?

Accepted Answer

$$y = 2^x$$

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

Solve the system of equations: $$\begin{cases} x + y = 5 \ x - y = 1 \end{cases}$$

Accepted Answer

$$x = 3, y = 2$$

Question 8

Which of the following is the correct solution to the inequality $$2x - 5 \u003e 7$$?

Accepted Answer

$$x \u003e 6$$

Question 9

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

Accepted Answer

$$25$$

Question 10

Which of the following is the correct logarithmic form of the equation $$8 = 2^x$$?

Accepted Answer

$$x = \log_2$ 8$$

Question 11

A company’s revenue $$R (in $$thousands of dollars) is modeled by $$R(x) = -2x^2$ + 12x + 10$$, where $$x is $$the number of units sold (in hundreds). What is the maximum revenue?

Accepted Answer

$$46$$ thousand dollars

Question 12

Which of the following is the domain of the function $$f(x) = \frac{1}{x-3}$$?

Accepted Answer

$$x 
eq 3$$

Question 13

Which transformation occurs when the graph of $$y = x^2$ is changed to y$$ = $$(x-4)^2 + 2$?

Accepted Answer

Shift right 4 units and up 2 units

Question 14

Which of the following is a solution to the equation $$\log_3$(x) = 2$$?

Accepted Answer

$$x = 9$$

Question 15

If $$f(x) = 2x + 1$$ and $$f^{-1}(x$$)$$ is the inverse, what is f$$^{-1}$$(5)$$?

Accepted Answer

$$2$$

Question 16

A car depreciates in value by 15% each year. If the car is worth $$20,000$$ now, what will its value be in 3 years? (Round to the nearest dollar)

Accepted Answer

$$12,239$$

Question 17

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

Accepted Answer

$$(0, \infty)$$

Question 18

Which of the following is the solution to the quadratic equation $$x^2 - 5x + 6 = 0$?

Accepted Answer

$$x = 2 or$$ $$x = 3$$

Question 19

Which of the following is the correct solution to the rational equation $$\frac{2}{x} = 4$$?

Accepted Answer

$$x = 0.5$$

Question 20

A radioactive substance decays according to the formula $$A = A_0$ e$$^{-0.2t}$$, where A_0$ is the initial amount and t$ is time in years. If A_0$ = 100$$ grams, how much remains after 5 years? (Round to the nearest gram)

Accepted Answer

$$37$$ grams

College Algebra Syllabus and Course Structure – Study Guide

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