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

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

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

$$\begin{bmatrix} 3 & 1 \\ 3 & 5 \end{bmatrix}$$

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

$$\begin{bmatrix} 4 & 6 \\ 1 & 3 \end{bmatrix}$$

Question 1

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

Accepted Answer

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

Question 2

Given the function $$f(x) = |2x - 6|$$, which of the following represents the solution set to the inequality $$f(x) \u003c 8$$?

Accepted Answer

$$-1 \u003c x \u003c 7$$

Question 3

Which of the following is the correct partial fraction decomposition for $$\frac{5x+3}{(x-1)(x+2)}$$?

Accepted Answer

$$\frac{3}{x-1} + \frac{2}{x+2}$$

Question 4

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

Accepted Answer

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

Question 5

Which of the following is the correct domain for the function $$f(x) = \log_2$(x-5)$$?

Accepted Answer

$$x \u003e 5$$

Question 6

Solve the equation $$2^{x+1} = 16$ for x$.

Accepted Answer

$$x = 3$$

Question 7

Which of the following is the sum of the first 10 terms of the arithmetic sequence where $$a_1 = 7$ and d = 3$?

Accepted Answer

$$175$$

Question 8

Given the system of equations: $$\begin{cases} x + 2y = 5 \ 3x - y = 4 \end{cases}$$, what is the solution $$(x, y)$$?

Accepted Answer

$$(2, 1.5)$$

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

$$3$$

Question 11

Which of the following is the correct expansion of $$(x+2)^3$$ using the Binomial Theorem?

Accepted Answer

$$x^3$$ + $$6x^2 + 12x + 8$

Question 12

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

Accepted Answer

$$x \u003e 2 or$$ $$x \u003c -1$$

Question 13

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

Accepted Answer

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

Question 14

Given the geometric sequence $$2, 6, 18, \ldots$$, what is the sum of the first 4 terms?

Accepted Answer

$$80$$

Question 15

Which of the following is the correct equation for a hyperbola centered at the origin with vertices at $$(\pm 4, 0)$$ and foci at $$(\pm 5, 0)$$?

Accepted Answer

$$\frac{x^2$}{16} - \frac{y^2$}{9} = 1$$

Question 16

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

Accepted Answer

$$\begin{bmatrix} 3 & 1 \ 3 & 5 \end{bmatrix}$$

Question 17

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

Accepted Answer

$$x = 6$$

Question 18

Which of the following is the correct result of multiplying the matrices $$\begin{bmatrix} 1 & 2 \ 0 & 1 \end{bmatrix}$$ and $$\begin{bmatrix} 2 & 0 \ 1 & 3 \end{bmatrix}$$?

Accepted Answer

$$\begin{bmatrix} 4 & 6 \ 1 & 3 \end{bmatrix}$$

MAC1140 Precalculus Algebra: Syllabus and Core Study Guide

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