Q: Which of the following is the sum of the matrices $$\begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$$ and $$\begin{pmatrix} 4 & 3 \\ 2 & 1 \end{pmatrix}$$?

$$\begin{pmatrix} 5 & 5 \\ 5 & 5 \end{pmatrix}$$

Q: Which of the following describes the end behavior of the polynomial $$f(x) = -2x^5$ + 3x^3$ - x + 7$$?

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

Q: If $$A = \begin{pmatrix} 2 & 1 \\ 0 & 3 \end{pmatrix}$$ and $$B = \begin{pmatrix} 1 & 0 \\ 4 & 2 \end{pmatrix}$$, what is $$AB$$?

$$\begin{pmatrix} 6 & 2 \\ 12 & 6 \end{pmatrix}$$

Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{2x - 8}$$?

Accepted Answer

$$x \geq 4$$

Question 2

A company’s revenue $$R (in $$thousands of dollars) from selling $$x$$ units of a product is modeled by $$R(x) = 5x - 0.01x^2$. What is the maximum revenue, and for how many units is it achieved?

Accepted Answer

Maximum revenue is $$125$$ thousand dollars at $$x = 250$$ units.

Question 3

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

Accepted Answer

$$11$$

Question 4

Which of the following equations represents a line perpendicular to $$y = -\frac{1}{2}x + 4$$ and passing through the point $$(2, 3)$$?

Accepted Answer

$$y - 3 = 2(x - 2)$$

Question 5

If $$f(x) = 3x - 7$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

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

Question 6

A population of bacteria triples every 4 hours. If the initial population is 200, which function models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P(t) = 200 \cdot 3$$^{t/4}$$

Question 7

Solve for $$x$$: $$2^{x+1} = 16$

Accepted Answer

$$x = 3$$

Question 8

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

Accepted Answer

$$x = 9$$

Question 9

Given the system of equations:

$$\begin{cases} 2x + 3y = 7 \ 4x - y = 5 \end{cases}$$

What is the solution $$(x, y)$$?

Accepted Answer

$$(2, 1)$$

Question 10

Which of the following is the sum of the matrices $$\begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix}$$ and $$\begin{pmatrix} 4 & 3 \ 2 & 1 \end{pmatrix}$$?

Accepted Answer

$$\begin{pmatrix} 5 & 5 \ 5 & 5 \end{pmatrix}$$

Question 11

A quadratic function models the height $$h (in $$meters) of a ball thrown upward from the ground as $$h(t) = -4.9t^2$ + 19.6t. At $$what time does the ball reach its maximum height?

Accepted Answer

$$t = 2$$ seconds

Question 12

Which of the following is the correct factorization of $$x^3$$ - $$4x^2 - 7x + 10$?

Accepted Answer

$$(x - 5)(x + 1)(x - 2)$$

Question 13

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

Accepted Answer

$$13$$

Question 14

Which of the following describes the end behavior of the polynomial $$f(x) = -2x^5$ + 3x^3$ - x + 7$$?

Accepted Answer

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

Question 15

A car depreciates in value by 15% each year. If its current value is $$V_0$$, which function models its value $$V(t)$$ after $$t$$ years?

Accepted Answer

$$V(t) = V_0$ \cdot (0.85)^t$$

Question 16

Which of the following is the solution to the equation $$\frac{2}{x} + 1 = 3$$?

Accepted Answer

$$x = 1$$

Question 17

If $$A = \begin{pmatrix} 2 & 1 \ 0 & 3 \end{pmatrix}$$ and $$B = \begin{pmatrix} 1 & 0 \ 4 & 2 \end{pmatrix}$$, what is $$AB$$?

Accepted Answer

$$\begin{pmatrix} 6 & 2 \ 12 & 6 \end{pmatrix}$$

Question 18

Which of the following is the sum of the infinite geometric series $$6 + 3 + 1.5 + \ldots$$?

Accepted Answer

$$12$$

Question 19

A quadratic equation $$ax^2 + bx + c = 0$ has real and equal roots. Which condition must be satisfied?

Accepted Answer

$$b^2 - 4ac = 0$

College Algebra Syllabus Study Guide

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