Question 1

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

Accepted Answer

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

Question 2

A ball is thrown upward from the top of a 50-meter building with an initial velocity of $$20 m/s. $$Its height $$h (in $$meters) after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 20t + 50. $$What is the maximum height the ball reaches?

Accepted Answer

$$70.41$$ meters

Question 3

Which of the following is the solution set for the inequality $$|2x - 5| \u003c 7$$?

Accepted Answer

$$ -1 \u003c x \u003c 6 $$

Question 4

Given $$f(x) = 2x^2$ - 3x + 1$$, what is the average rate of change of $$f$$ from $$x = 1 to$$ $$x = 4$$?

Accepted Answer

$$11$$

Question 5

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$ + 4$$

Question 6

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 7

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

Accepted Answer

The domain is $$x \u003e 0$$ and the range is $$(-\infty, \infty).$$

Question 8

If $$f(x) = 3x - 2$$ and $$g(x) = x^2$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$3 \cdot 4 - 2 = 10$$

Question 9

Which of the following is the inverse of $$f(x) = 2x + 5$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 5}{2}$$

Question 10

A right triangle has legs of length $$7$$ and $$24. $$What is the length of the hypotenuse?

Accepted Answer

$$25$$

Question 11

Which of the following is the correct equation for the vertical asymptote of the function $$f(x) = \frac{2x}{x^2$ - 9}$$?

Accepted Answer

$$x = 3$$ and $$x = -3$$

Question 12

If $$\sin(	heta) = \frac{1}{2}$$ and $$0 \u003c 	heta \u003c \pi$$, what is $$	heta in $$radians?

Accepted Answer

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

Question 13

Which of the following is equivalent to $$\log_{2}(8) + \log_{2}(4)$$?

Accepted Answer

$$5$$

Question 14

A sector of a circle has a radius of $$10 cm $$and a central angle of $$\frac{\pi}{3}$$ radians. What is the area of the sector?

Accepted Answer

$$\frac{50\pi}{3} cm$^2$$

Question 15

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

Accepted Answer

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

Question 16

If $$	an(\alpha) = 3$$ and $$\alpha is in $$the first quadrant, what is $$\sin(\alpha)$$?

Accepted Answer

$$\frac{3}{\sqrt{10}}$$

Question 17

Which transformation maps the graph of $$y = f(x) to$$ $$y = -2f(x + 3)$$?

Accepted Answer

Shift left by $$3$$ units, reflect across the $$x-$$axis, and vertically stretch by $$2$$

Question 18

If $$f(x) = x^2$ - 4x + 7$$, what is the vertex of the parabola?

Accepted Answer

$$(2, 3)$$

Question 19

A radioactive substance has a half-life of $$10$$ years. If the initial amount is $$80$$ grams, how much remains after $$30$$ years?

Accepted Answer

$$10$$ grams

Question 20

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

Accepted Answer

$$x = \log_{2} 7$$

Comprehensive Precalculus Final Exam Study Guide

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