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

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

Q: If $$f(x) = x^3$ - 4x^2$ + x + 6$$, what is the remainder when $$f(x) is $$divided by $$x-2$$?

$$f(2) = 2^3$ - 4 \times 2^2$ + 2 + 6 = 8 - 16 + 2 + 6 = 0$$

Question 1

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

Accepted Answer

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

Question 2

A pharmaceutical company models the concentration of a drug in the bloodstream by $$C(t) = 50e$$^{-0.2t}$$, where t$ is time in hours. What is the concentration after 5 hours?

Accepted Answer

$$C(5) = 50e$$^{-1}$$ \approx 18.4$$

Question 3

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

Accepted Answer

$$\frac{5x+3}{(x+1)(x-2)} = \frac{8}{x+1} - \frac{3}{x-2}$$

Question 4

If $$f(x) = |2x - 5|$$, which of the following represents the solution set to $$f(x) \u003c 7$$?

Accepted Answer

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

Question 5

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

Accepted Answer

$$500 	imes 2^3$ = 4000$$

Question 6

Which of the following is the correct equation for an ellipse centered at the origin with a major axis along the $$x-$$axis, $$a = 5$$, and $$b = 3$$?

Accepted Answer

$$\frac{x^2$}{25} + \frac{y^2$}{9} = 1$$

Question 7

Given the arithmetic sequence with first term $$a_1 = 7$ and common difference d = 4$, what is the 10th term?

Accepted Answer

$$a_{10} = 43$$

Question 8

Which of the following is the correct solution to the system of equations using Cramer's Rule?

$$\begin{cases} 2x + 3y = 8 \ x - y = 2 \end{cases}$$

Accepted Answer

Question 9

Which of the following is the correct domain for the function $$f(x) = \log_{2}(x-3)$$?

Accepted Answer

$$x \u003e 3$$

Question 10

A rational function $$f(x) = \frac{2x^2$ + 3x - 5}{x^2$ - 4}$$ has which of the following vertical asymptotes?

Accepted Answer

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

Question 11

Which of the following is the correct sum of the first 5 terms of the geometric sequence $$a_1 = 3$, r = 2$?

Accepted Answer

$$93$$

Question 12

If $$f(x) = x^3$ - 4x^2$ + x + 6$$, what is the remainder when $$f(x) is $$divided by $$x-2$$?

Accepted Answer

$$f(2) = 2^3$ - 4 	imes 2^2$ + 2 + 6 = 8 - 16 + 2 + 6 = 0$$

Question 13

Which of the following is the correct solution to the exponential equation $$3^{x} = 81$?

Accepted Answer

$$x = 4$$

Question 14

Which of the following is the correct formula for the sum of the first $$n$$ terms of an arithmetic sequence?

Accepted Answer

$$S_n = \frac{n}{2}(a_1$ + a_n)$$

Question 15

Which of the following is the correct transformation for the function $$f(x) = x^2$ shifted 3 units right and 2 units up?

Accepted Answer

$$f(x) = (x-3)^2$ + 2$$

Question 16

Which of the following is the correct solution to the logarithmic equation $$\log_{10}(x) = 2$$?

Accepted Answer

$$x = 100$$

Question 17

Which of the following is the correct formula for the sum of an infinite geometric series with $$|r| \u003c 1$$?

Accepted Answer

$$S = \frac{a_1$}{1 - r}$$

Question 18

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

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

MAC1140 Precalculus Algebra: Syllabus and Core Study Guide

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