Question 1

Which of the following equations has no real solution?

Accepted Answer

$$x^2 + 4 = 0$

Question 2

A ball is thrown upward from a height of 2 meters with an initial velocity of 10 m/s. Its height after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 10t + 2. $$What is the maximum height the ball reaches?

Accepted Answer

$$7.1$$ meters

Question 3

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$

Question 4

Given the circle $$x^2$$ + $$y^2 - 6x + 8y = 0$, what are the coordinates of its center?

Accepted Answer

$$(3, -4)$$

Question 5

Which of the following is the correct equation of the line passing through $$(2, -1)$$ and parallel to $$y = 3x + 5$$?

Accepted Answer

$$y = 3x - 7$$

Question 6

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

Accepted Answer

$$9$$

Question 7

Which of the following statements about the function $$f(x) = \ln(x) is $$true?

Accepted Answer

The domain is $$(0, \infty)$$

Question 8

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

Accepted Answer

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

Question 9

Which of the following is the solution set for $$|2x - 3| \u003c 5$$?

Accepted Answer

$$-1 \u003c x \u003c 4$$

Question 10

What is the average rate of change of $$f(x) = x^2$ from x = 1$ to x = 4$?

Accepted Answer

$$5$$

Question 11

Which of the following is the correct inverse of $$f(x) = 3x - 2$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x + 2}{3}$$

Question 12

If $$\sin(	heta) = \frac{1}{2}$$ and $$0 \leq 	heta \u003c 2\pi$$, what are all possible values of $$	heta$$?

Accepted Answer

$$\frac{\pi}{6}, \frac{5\pi}{6}$$

Question 13

Which of the following is a true statement about the graph of $$y = \cos(x)$$?

Accepted Answer

It is an even function and symmetric about the $$y-$$axis.

Question 14

A right triangle has legs of length 5 and 12. What is the length of the hypotenuse?

Accepted Answer

$$13$$

Question 15

Which of the following is the correct simplification of $$\log_{2}(8x)$$?

Accepted Answer

$$3 + \log_{2}(x)$$

Question 16

If $$f(x) = x^3$ - 2x^2$ + x - 2$$, which of the following is a root of $$f(x)$$?

Accepted Answer

$$2$$

Question 17

A radioactive substance decays according to $$P(t) = P_0$ e$$^{-0.2t}$$. What is the half-life of the substance (rounded to the nearest tenth)?

Accepted Answer

$$3.5$$

Question 18

Which of the following is the correct solution to $$2^{x} = 10$?

Accepted Answer

$$x = \log_{2}(10)$$

Question 19

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

Accepted Answer

$$(x + 1)^2$

Question 20

Which of the following is the correct equation for the horizontal asymptote of $$f(x) = \frac{3x^2$ + 2}{x^2$ - 5}$$?

Accepted Answer

$$y = 3$$

Comprehensive Precalculus Final Exam Study Guide

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