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

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 solution to the equation $$2(x - 3) = 4x + 6$$?

Accepted Answer

$$x = -3$$

Question 2

Simplify the expression $$\left( x$$^{\frac{3}$${2}} \right) \cdot \left( x$$^{\frac{1}$${2}} \right).$$

Accepted Answer

$$x^2$$

Question 3

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

Accepted Answer

Question 4

A ball is thrown upward and its height in meters after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 20t + 1.5. $$After how many seconds does the ball reach its maximum height?

Accepted Answer

$$t = 2.04$$

Question 5

Which of the following is NOT in the domain of the function $$f(x) = \frac{2x}{x^2$ - 9}$$?

Accepted Answer

$$x = 3$$

Question 6

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

Accepted Answer

$$9$$

Question 7

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

Accepted Answer

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

Question 8

Which of the following is the correct simplified form of $$\frac{x^2$ - 9}{x^2$ - 6x + 9}$$?

Accepted Answer

$$\frac{(x+3)(x-3)}{(x-3)^2$}$$

Question 9

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

Accepted Answer

$$(-\infty, 6)$$

Question 10

If $$f(x) is an $$even function, which of the following must be true?

Accepted Answer

$$f(-x) = f(x)$$

Question 11

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

Accepted Answer

$$x \geq 2$$

Question 12

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

Accepted Answer

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

Question 13

Which of the following is the correct value of $$\log_2$ 32$$?

Accepted Answer

$$5$$

Question 14

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

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

Which of the following is the correct value of $$\sin 45^\circ$$?

Accepted Answer

$$\frac{\sqrt{2}}{2}$$

Question 17

Which of the following is the correct radian measure for $$120^\circ$$?

Accepted Answer

$$\frac{2\pi}{3}$$

Question 18

Which of the following is the correct parent function for a parabola opening upwards?

Accepted Answer

$$f(x) = x^2$

Question 19

Which of the following is the correct equation for the horizontal asymptote of $$f(x) = \frac{2x^2$ + 1}{x^2$ - 3}$$?

Accepted Answer

$$y = 2$$

Question 20

If $$f(x) = x^2$ and g(x) = x + 1$, what is the difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$2x + h$$

Math113 Precalculus: Structured Study Guide (Fall 2026)

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