Q: Which of the following describes the end behavior of the polynomial $$f(x) = -2x^4$ + 5x^2$ - 7$$?

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 definition of a function?

Accepted Answer

A relation where each input is paired with exactly one output.

Question 2

Given the function $$f(x) = 2x^2$ - 3x + 5$$, what is $$f(-2)$$?

Accepted Answer

$$f(-2) = 17$$

Question 3

Which of the following equations represents a line with a slope of $$-4$$ and a $$y-$$intercept of $$3$$?

Accepted Answer

$$y = -4x + 3$$

Question 4

Solve the quadratic equation $$x^2 - 5x + 6 = 0$.

Accepted Answer

$$x = 2 or$$ $$x = 3$$

Question 5

What is the domain of the function $$f(x) = \frac{1}{x-4}$$?

Accepted Answer

$$x 
eq 4$$

Question 6

Which of the following is the inverse of the function $$f(x) = 3x + 2$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-2}{3}$$

Question 7

A population of bacteria doubles every 3 hours. If the initial population is 200, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P = 200 \cdot 2$$^{t/3}$$

Question 8

Solve the system of equations: $$\begin{cases} x + y + z = 6 \ 2x - y + 3z = 14 \ -x + 4y - z = -2 \end{cases}$$

Accepted Answer

$$x = 2, y = 1, z = 3$$

Question 9

Which of the following describes the end behavior of the polynomial $$f(x) = -2x^4$ + 5x^2$ - 7$$?

Accepted Answer

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

Question 10

Which of the following is the correct application of the change of base formula for $$\log_5$ 20$$?

Accepted Answer

$$\log_5$ 20 = \frac{\log_{10} 20}{\log_{10} 5}$$

Question 11

A company’s profit $$P (in $$dollars) from selling $$x$$ units is modeled by $$P(x) = -2x^2$ + 400x - 5000. $$What is the maximum profit, and how many units should be sold to achieve it?

Accepted Answer

Maximum profit is $$35,000 at$$ $$x = 100$$ units.

Question 12

Which transformation is applied to the graph of $$y = x^2$ to obtain y$$ = $$(x-3)^2 + 2$?

Accepted Answer

Shift right 3 units and up 2 units.

Question 13

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

Accepted Answer

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

Question 14

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

Accepted Answer

$$(f \circ g)(2) = 9$$

Question 15

Which of the following is the correct graph for the rational function $$f(x) = \frac{2x}{x-1}$$?

Accepted Answer

Vertical asymptote at $$x = 1$$, horizontal asymptote at $$y = 0$$

Question 16

Which of the following is equivalent to $$\sqrt[3]{x^6$}$$?

Accepted Answer

Question 17

Which of the following is the correct solution to the exponential equation $$2^{x+1} = 16$?

Accepted Answer

$$x = 3$$

Question 18

A radioactive substance decays according to $$A(t) = 100e$$^{-0.05t}$$, where A$ is the amount remaining after t$ years. How much remains after 10 years?

Accepted Answer

$$A(10) = 60.65$$

MAC 1105 College Algebra – Course Syllabus and Core Topics Study Guide

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