Q: Which of the following matrices is the inverse of $$A = \begin{pmatrix} 2 & 0 \\ 0 & 3 \end{pmatrix}$$?

$$A^{-1}$$ = \begin{pmatrix} \frac{1}{2} & 0 \\ 0 & \frac{1}{3} \end{pmatrix}$$

Q: Which of the following statements is TRUE about the end behavior of the polynomial $$f(x) = -2x^4$ + 5x^2$ - 3$$?

As $$x \to \infty$$, $$f(x) \to -\infty$$; as $$x \to -\infty$$, $$f(x) \to -\infty$$

Question 1

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

Accepted Answer

All real numbers except $$x = 3$$

Question 2

A function $$f(x) is $$defined as $$f(x) = 2x^2$ - 5x + 1. $$What is the range of $$f(x)$$?

Accepted Answer

All real numbers less than or equal to $$\frac{9}{8}$$

Question 3

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

Accepted Answer

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

Question 4

A chemical reaction is modeled by the exponential function $$N(t) = N_0$ e$$^{-kt}$$, where N_0$ is the initial amount and k$ is a positive constant. If N_0$ = 100$$ and $$k = 0.05$$, how much of the substance remains after 20 minutes?

Accepted Answer

$$N(20) = 100 e$$^{-1}$$

Question 5

Which of the following is NOT a function?

Accepted Answer

A relation where an input is paired with two different outputs

Question 6

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

Accepted Answer

$$(f \circ g)(x) = (x + 1)^2$

Question 7

A rational function $$f(x) = \frac{2x^2$ + 3x - 2}{x^2$ - 4}$$ has which vertical asymptotes?

Accepted Answer

$$x = 2$$ and $$x = -2$$

Question 8

Which property of logarithms allows you to write $$\log_b(MN) as$$ $$\log_b(M) + \log_b(N)$$?

Accepted Answer

Product property

Question 9

A population of bacteria doubles every 3 hours. If the initial population is 500, which equation models the population after $$t$$ hours?

Accepted Answer

$$P(t) = 500 \cdot 2$$^{\frac{t}$${3}}$$

Question 10

Solve the equation $$2^{x} = 32$ for x$.

Accepted Answer

$$x = 5$$

Question 11

Which of the following matrices is the inverse of $$A = \begin{pmatrix} 2 & 0 \ 0 & 3 \end{pmatrix}$$?

Accepted Answer

$$A^{-1}$$ = \begin{pmatrix} \frac{1}{2} & 0 \ 0 & \frac{1}{3} \end{pmatrix}$$

Question 12

If $$f(x) = \sqrt{x-1}$$, what is the domain of $$f$$?

Accepted Answer

$$x \geq 1$$

Question 13

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

Accepted Answer

$$x = 3, y = 2$$

Question 14

Which of the following statements is TRUE about the end behavior of the polynomial $$f(x) = -2x^4$ + 5x^2$ - 3$$?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o -\infty$$; as $$x 	o -\infty$$, $$f(x) 	o -\infty$$

Question 15

A medical dosage is modeled by $$D(t) = 50 e$$^{-0.1t}$$, where t$ is time in hours. What is the dosage after 10 hours?

Accepted Answer

$$D(10) = 50 e$$^{-1}$$

Question 16

Which of the following is the correct application of the vertical line test?

Accepted Answer

If any vertical line crosses the graph more than once, it is not a function.

Question 17

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

Accepted Answer

$$x = 8$$

Question 18

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

Accepted Answer

$$(f + g)(x) = x^2$ + 2x + 1$$

Question 19

Which of the following is the determinant of the matrix $$\begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix}$$?

Accepted Answer

$$-2$$

College Algebra Syllabus and Core Concepts Overview

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