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

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

Q: Which of the following is the correct solution for $$\sin(\theta) = \dfrac{1}{2}$$ for $$0 \leq \theta \u003c 2\pi$$?

$$\theta = \dfrac{\pi}{6}, \dfrac{5\pi}{6}$$

Question 1

Which of the following best describes the difference between a function and a relation?

Accepted Answer

A function assigns exactly one output to each input, while a relation can assign multiple outputs to a single input.

Question 2

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

Accepted Answer

$$f(-2) = 17$$

Question 3

A company models its profit $$P (in $$thousands of dollars) as a function of the number of units sold $$x by$$ $$P(x) = -2x^2$ + 40x - 100. $$What is the maximum profit, and how many units should be sold to achieve it?

Accepted Answer

Maximum profit is $$300 at$$ $$x = 10$$ units.

Question 4

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

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

Which of the following equations represents a circle with center at $$(2, -3)$$ and radius $$5$$?

Accepted Answer

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

Question 7

A population of bacteria doubles every 3 hours. If the initial population is 500, which function models the population $$P(t)$$ after $$t$$ hours?

Accepted Answer

$$P(t) = 500 \cdot 2$$^{t/3}$$

Question 8

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

Accepted Answer

$$x = 32$$

Question 9

Which of the following is the solution set for $$|2x - 3| \u003c 7$$?

Accepted Answer

$$-2 \u003c x \u003c 5$$

Question 10

A ball is thrown upward from the top of a building. Its height $$h (in $$meters) after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 24t + 30. $$After how many seconds does the ball reach its maximum height?

Accepted Answer

$$t = 2.45$$ seconds

Question 11

Which of the following is the correct factorization of $$x^2 - 9x + 20$?

Accepted Answer

$$(x - 4)(x - 5)$$

Question 12

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

Accepted Answer

All real numbers except $$x = 2$$

Question 13

Which of the following 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 14

Which of the following is the solution to the system of equations: $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$(x, y) = (2, 1)$$

Question 15

Which of the following is the correct equation for the line passing through the points $$(1, 2)$$ and $$(3, 8)$$?

Accepted Answer

$$y = 3x - 1$$

Question 16

A radioactive substance decays according to the formula $$A(t) = A_0$ e$$^{-0.2t}$$, where A_0$ is the initial amount. What is the half-life of the substance (rounded to the nearest tenth)?

Accepted Answer

$$t = 3.5$$

Question 17

Which of the following is the solution to the quadratic equation $$2x^2 - 4x - 6 = 0$?

Accepted Answer

$$x = 3, x = -1$$

Question 18

If $$f(x) = \sqrt{x - 1}$$, for which values of $$x is$$ $$f(x)$$ defined?

Accepted Answer

$$x \geq 1$$

Question 19

A car's value depreciates by 15\% each year. If the car is worth $$20,000 now, which function models its value V(t$$)$$ after t$ years?

Accepted Answer

$$V(t) = 20000 \cdot (0.85)^t$$

Question 20

Which of the following is the correct solution for $$\sin(	heta) = \dfrac{1}{2}$$ for $$0 \leq 	heta \u003c 2\pi$$?

Accepted Answer

$$	heta = \dfrac{\pi}{6}, \dfrac{5\pi}{6}$$

MAT 171 Precalculus Algebra: Course Schedule and Structure Overview

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