Question 1

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

Accepted Answer

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

Question 2

Solve the inequality $$2x^2 - 5x - 3$$ \u003c 0$$.

Accepted Answer

$$(-\frac{1}{2}, 3)$$

Question 3

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

Accepted Answer

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

Question 4

A population of bacteria triples every 4 hours. If the initial population is 200, which equation models the population $$P$$ after $$t$$ hours?

Accepted Answer

$$P = 200 \cdot 3$$^{t/4}$$

Question 5

Which of the following is the solution to the equation $$\log_2$(x-1) = 3$$?

Accepted Answer

$$x = 9$$

Question 6

Given $$f(x) = x^2$ - 4$$ and $$g(x) = 2x + 1$$, what is $$(f \circ g)(x)$$?

Accepted Answer

$$(2x + 1)^2$ - 4$$

Question 7

Which of the following is a possible rational root of $$f(x) = 2x^3$ - 5x^2$ + 4x - 1$$ according to the Rational Root Theorem?

Accepted Answer

$$\frac{1}{2}$$

Question 8

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

Accepted Answer

$$t = 0$$ and $$t = 2$$

Question 9

Which of the following is the correct factorization of $$x^3 - 8$?

Accepted Answer

$$(x - 2)(x^2$ + 2x + 4)$$

Question 10

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

Accepted Answer

$$x 
eq 3, x 
eq -3$$

Question 11

If $$\sin(	heta) = \frac{3}{5}$$ and $$	heta is in $$Quadrant II, what is $$\cos(	heta)$$?

Accepted Answer

$$-\frac{4}{5}$$

Question 12

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

Accepted Answer

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

Question 13

Solve for $$x$$: $$2^{x+1} = 16$.

Accepted Answer

$$x = 3$$

Question 14

Which of the following is the sum formula for sine?

Accepted Answer

$$\sin(A + B) = \sin A \cos B + \cos A \sin B$$

Question 15

Which of the following is the solution set for $$|2x - 5| = 7$$?

Accepted Answer

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

Question 16

A radioactive substance decays according to $$A(t) = A_0$ e$$^{-0.2t}$$. If the initial amount is 100$ grams, how much remains after 5$ hours?

Accepted Answer

$$A = 100e$$^{-1}$$

Question 17

Which of the following is the correct solution to the system: $$\begin{cases} x + y = 5 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$(x, y) = (3, 2)$$

Question 18

Which of the following is the correct equation for the graph of a parabola opening downward with vertex at $$(0, 4)$$?

Accepted Answer

$$y = -x^2$ + 4$$

Question 19

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

Accepted Answer

$$x \geq 2$$

Question 20

Which of the following is the correct expression for the sum of a geometric series with first term $$a$$ and common ratio $$r$$ ($$r 
eq 1) $$for $$n$$ terms?

Accepted Answer

$$S_n = a \frac{1 - r^n}{1 - r}$$

Precalculus Syllabus and Study Guide: Course Structure, Topics, and Learning Outcomes

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