Q: Which of the following is the correct simplification of $$\dfrac{2x^2$ - 8}{x^2$ - 4}$$?

$$\dfrac{2(x - 2)}{x + 2}$$, for $$x \neq 2, x \neq -2$$

Q: Which of the following is the correct result of multiplying the matrices $$A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$$ and $$B = \begin{pmatrix} 2 & 0 \\ 1 & 2 \end{pmatrix}$$?

$$\begin{pmatrix} 4 & 4 \\ 10 & 8 \end{pmatrix}$$

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 $$x \to -\infty$$, $$f(x) \to \infty$$

Question 1

Which of the following is the correct simplification of $$\sqrt[3]{x^6$ y^3$}$$ for all real $$x$$ and $$y$$?

Accepted Answer

$$x^2 y$

Question 2

A quadratic equation models the height $$h (in $$meters) of a ball thrown upward from a building as $$h(t) = -4.9t^2$ + 20t + 50. $$What is the maximum height the ball reaches?

Accepted Answer

$$70.41$$ meters

Question 3

Which of the following is the solution set for the inequality $$|2x - 5| \u003c 7$$?

Accepted Answer

$$-1 \u003c x \u003c 6$$

Question 4

Given $$f(x) = 2x^2$ - 3x + 1$$, which of the following is $$f^{-1}(x$$)$$, the inverse function, if it exists?

Accepted Answer

The function $$f(x)$$ does not have an inverse over all real numbers.

Question 5

Which of the following is the correct factorization of $$x^4 - 16$?

Accepted Answer

$$(x - 2)(x + 2)(x^2$ + 4)$$

Question 6

A company’s revenue $$R (in $$thousands of dollars) is modeled by $$R(x) = -2x^2$ + 12x + 20$$, where $$x is $$the number of units sold (in thousands). What is the maximum revenue, and for how many units sold does it occur?

Accepted Answer

Maximum revenue is $$56$$ thousand dollars at $$x = 3$$ thousand units.

Question 7

Which of the following is the solution to the system of equations: $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$x = 2, y = 1$$

Question 8

Which of the following is the correct simplification of $$\dfrac{2x^2$ - 8}{x^2$ - 4}$$?

Accepted Answer

$$\dfrac{2(x - 2)}{x + 2}$$, for $$x 
eq 2, x 
eq -2$$

Question 9

If $$f(x) = 3x - 5$$ and $$g(x) = x^2$ + 2$$, what is $$(f \circ g)(2)$$?

Accepted Answer

Question 10

Which of the following is the correct solution to the equation $$2^{x} = 32$?

Accepted Answer

$$x = 5$$

Question 11

A circle has endpoints of a diameter at $$(2, 3)$$ and $$(8, 11). $$What is the equation of the circle?

Accepted Answer

$$(x - 5)^2$ + (y - 7)^2$ = 50$$

Question 12

Which of the following is the correct solution to the logarithmic equation $$\log_3$(x - 1) = 2$$?

Accepted Answer

$$x = 10$$

Question 13

Which of the following is the correct result of multiplying the matrices $$A = \begin{pmatrix} 1 & 2 \ 3 & 4 \end{pmatrix}$$ and $$B = \begin{pmatrix} 2 & 0 \ 1 & 2 \end{pmatrix}$$?

Accepted Answer

$$\begin{pmatrix} 4 & 4 \ 10 & 8 \end{pmatrix}$$

Question 14

Which of the following is the correct solution to the rational equation $$\dfrac{x}{x - 2} = 3$$?

Accepted Answer

Question 15

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 16

A population of bacteria doubles every 3 hours. If the initial population is 500, what will the population be after 9 hours?

Accepted Answer

$$4000$$

Question 17

Which of the following is the correct solution to the inequality $$\dfrac{x + 2}{x - 1} \u003e 0$$?

Accepted Answer

$$x  1$$

Question 18

Which of the following is the correct result of $$\log_{2} 32$$?

Accepted Answer

$$5$$

College Algebra (MATH 1030) Syllabus and Study Guide

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