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

$$f(x) \to -\infty as$$ $$x \to \infty$$ and $$f(x) \to \infty as$$ $$x \to -\infty$$

Question 1

Which of the following equations represents a quadratic equation?

Accepted Answer

$$x^2 + 5x - 6 = 0$

Question 2

Given the function $$f(x) = 2x^2$ - 3x + 1$$, what is the vertex of its graph?

Accepted Answer

$$(\frac{3}{4}, -\frac{1}{8})$$

Question 3

Which of the following is the correct solution to the equation $$|2x - 5| = 7$$?

Accepted Answer

$$x = 6,\ x = -1$$

Question 4

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 5

Which of the following is the inverse of the function $$f(x) = 3x + 4$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 4}{3}$$

Question 6

Solve the system of equations: $$\begin{cases} 2x + y = 7 \ x - y = 1 \end{cases}$$

Accepted Answer

$$x = 2,\ y = 3$$

Question 7

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

Accepted Answer

$$f(x) 	o -\infty as$$ $$x 	o \infty$$ and $$f(x) 	o \infty as$$ $$x 	o -\infty$$

Question 8

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

Accepted Answer

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

Question 9

Which of the following is the correct domain for the function $$f(x) = \frac{1}{x-3}$$?

Accepted Answer

$$(-\infty, 3) \cup (3, \infty)$$

Question 10

A radioactive substance decays according to the formula $$A = A_0$ e$$^{-0.2t}$$, where A_0$ is the initial amount and t$ is time in years. If A_0$ = 100$$ grams, how much remains after 5 years?

Accepted Answer

$$A = 100 e$$^{-1}$$ \approx 36.79$$ grams

Question 11

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

Accepted Answer

$$x \u003c 6$$

Question 12

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

Accepted Answer

$$[2, \infty)$$

Question 13

Which of the following is the correct logarithmic form of the equation $$5^x = 125$$?

Accepted Answer

$$x = \log_5$ 125$$

Question 14

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

Accepted Answer

$$(f + g)(3) = 12$$

Question 15

Which of the following describes the graph of $$y = |x - 2| + 3$$?

Accepted Answer

A V-shaped graph with vertex at $$(2, 3)$$

Question 16

Which of the following is the correct solution to the equation $$\log_2$(x) = 5$$?

Accepted Answer

$$x = 32$$

Question 17

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?

Accepted Answer

$$R = 56$$ thousand dollars

College Algebra MAC 1105 Syllabus and Course Overview

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