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

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

Question 1

Which of the following best describes the solution set for the equation $$2x^2 - 8x + 6 = 0$?

Accepted Answer

Question 2

A company models its profit $$P (in $$thousands of dollars) as a function of the number of units sold $$x by$$ $$P(x) = -2x^2$ + 12x - 10. $$What is the maximum profit, and how many units should be sold to achieve it?

Accepted Answer

Maximum profit is $$8 at$$ $$x = 3$$

Question 3

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 4

Given $$f(x) = x^2$ and g(x) = x + 2$, what is the domain of the composite function f(g(x$$))$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 5

A radioactive substance decays according to the formula $$A(t) = 100e$$^{-0.05t}$$, where A$ is the amount remaining after t$ years. How much remains after 20 years?

Accepted Answer

$$A(20) = 100e$$^{-1}$$ \approx 36.79$$

Question 6

Which of the following is the correct solution to the inequality $$3x - 5 \u003c 10$$?

Accepted Answer

$$x \u003c 5$$

Question 7

If $$f(x) = \sqrt{x - 2}$$, what is the domain of $$f$$?

Accepted Answer

$$[2, \infty)$$

Question 8

Which of the following equations represents a line parallel to $$y = 2x + 3$$ and passing through the point $$(1, 4)$$?

Accepted Answer

$$y = 2x + 2$$

Question 9

Solve for $$x$$: $$\log_2$(x) = 5$$

Accepted Answer

$$x = 32$$

Question 10

A quadratic equation has roots at $$x = -3$$ and $$x = 5. $$Which of the following is the correct equation?

Accepted Answer

$$x^2 - 2x - 15 = 0$

Question 11

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

Accepted Answer

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

Question 12

Which of the following is the correct simplification of $$\sqrt{50}$$?

Accepted Answer

$$2\sqrt{5}$$

Question 13

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

Accepted Answer

$$19$$

Question 14

Which of the following is the correct solution to $$|2x - 3| = 7$$?

Accepted Answer

$$x = 5 or$$ $$x = -2$$

Question 15

A population of bacteria doubles every 4 hours. If the initial population is 500, what is the population after 12 hours?

Accepted Answer

$$4000$$

Question 16

Which of the following is the correct factorization of $$x^2 - 9$?

Accepted Answer

$$(x - 3)(x + 3)$$

Question 17

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

Accepted Answer

$$x = 4$$

Question 18

If $$f(x) = \frac{1}{x-2}$$, what is the domain of $$f$$?

Accepted Answer

$$(-\infty, 2) \cup (2, \infty)$$

Question 19

Which of the following is the correct solution to $$x^2 + 6x + 9 = 0$?

Accepted Answer

$$x = -3$$

College Algebra Syllabus and Course Overview – Perimeter College at Georgia State University

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