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

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 to $$\cos(\theta) = \frac{1}{2}$$ for $$0 \leq \theta \u003c 2\pi$$?

$$\theta = \frac{\pi}{3}, \frac{5\pi}{3}$$

Question 1

Which of the following is the correct result of dividing $$2x^3$$ - $$3x^2 + 4x - 5$ by x - 2$ using synthetic division?

Accepted Answer

$$2x^2 + x + 6$ with a remainder of 7$

Question 2

Which of the following intervals represents the solution set to the inequality $$3x - 7 \u003c 2x + 5$$?

Accepted Answer

Question 3

Given the points $$A(2, 3)$$ and $$B(-4, 7)$$, what is the distance between $$A$$ and $$B$$?

Accepted Answer

$$\sqrt{52}$$

Question 4

Which of the following equations represents a circle with center at $$(1, -2)$$ and radius $$5$$?

Accepted Answer

$$(x - 1)^2$ + (y + 2)^2$ = 25$$

Question 5

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

Accepted Answer

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

Question 6

A population of bacteria doubles every 4 hours. If the initial population is 500, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P = 500 \cdot 2$$^{t/4}$$

Question 7

Which of the following is the correct solution to the equation $$\log_3$(x - 2) = 4$$?

Accepted Answer

Question 8

Which of the following is the correct domain of the function $$f(x) = \frac{1}{x^2$ - 9}$$?

Accepted Answer

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

Question 9

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

Accepted Answer

$$9$$

Question 10

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

Accepted Answer

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

Question 11

Which of the following is the correct solution to $$2^{x+1} = 32$?

Accepted Answer

$$x = 4$$

Question 12

Which of the following is the correct equation for the graph of $$y = \sin(x)$$ shifted right by $$\frac{\pi}{2}$$ units?

Accepted Answer

$$y = \sin(x - \frac{\pi}{2})$$

Question 13

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

Accepted Answer

$$	heta = \frac{\pi}{3}, \frac{5\pi}{3}$$

Question 14

A ball is thrown upward from the ground with an initial velocity of $$32 ft/s. $$Its height after $$t$$ seconds is given by $$h(t) = -16t^2$ + 32t. At $$what time does the ball reach its maximum height?

Accepted Answer

$$t = 1$$ second

Question 15

Which of the following is the correct solution to the equation $$	an(x) = 1$$ for $$0 \leq x \u003c 2\pi$$?

Accepted Answer

$$x = \frac{\pi}{4}, \frac{5\pi}{4}$$

Question 16

Which of the following is the correct range of the function $$f(x) = \sin(x) + 2$$?

Accepted Answer

$$[1, 3]$$

Question 17

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

Accepted Answer

$$x = 100$$

Question 18

Which of the following is the correct solution set for $$|2x - 3| \leq 5$$?

Accepted Answer

$$[-1, 4]$$

Question 19

Which of the following is the correct period of the function $$f(x) = 3\cos(2x)$$?

Accepted Answer

$$\pi$$

Question 20

Which of the following is the correct solution to the equation $$e^{2x} = 7$?

Accepted Answer

$$x = \frac{1}{2} \ln 7$$

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