Question 1

Given the functions $$f(x) = 4x + 12$$ and $$g(x) = 4x - 1$$, what is the domain of $$f + g$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 2

If $$f(x) = x^2$ + 2x + 5$$ and $$g(x) = 4x^2$ - 1$$, what is the domain of $$f \cdot g$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 3

Given $$f(x) = \sqrt{x-3}$$ and $$g(x) = x^2$ - 2$$, what is the domain of $$f \circ g$$?

Accepted Answer

$$(-\infty, -1] \cup [1, \infty)$$

Question 4

Which sequence of transformations must be applied to the graph of $$f(x) = x to $$obtain the graph of $$h(x) = -2(x-3) + 4$$?

Accepted Answer

Shift right 3, reflect over $$x-$$axis, stretch vertically by 2, shift up 4

Question 5

Solve for $$x$$: $$\log_3$(x-2) = 2$$

Accepted Answer

$$x = 11$$

Question 6

A population of bacteria triples every 4 hours. If the initial population is 200, how many bacteria will there be after 12 hours?

Accepted Answer

$$200 	imes 3^3$ = 5400$$

Question 7

A radioactive substance decays according to $$A(t) = 1000e$$^{-0.07t}$$, where t$ is in years. How long will it take for the substance to decay to 250 grams?

Accepted Answer

$$t = \frac{\ln(4)}{0.07}$$

Question 8

Find the exact value of $$\sin(150^\circ)$$ using the unit circle.

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

Given $$	an(	heta) = \frac{3}{4}$$ and $$	heta is in $$quadrant III, what is $$\sin(	heta)$$?

Accepted Answer

$$-\frac{3}{5}$$

Question 11

A Ferris wheel with a radius of 20 meters makes one complete revolution every 40 seconds. If a passenger starts at the lowest point, what is their height above the ground after 10 seconds, assuming the center is 22 meters above the ground?

Accepted Answer

$$22 + 20\sin\left(\frac{\pi}{2}\right) = 42$$ meters

Question 12

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

Accepted Answer

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

Question 13

If $$f(x) = \frac{1}{x-2}$$, what is the domain of $$f$$?

Accepted Answer

$$(-\infty, 2) \cup (2, \infty)$$

Question 14

Which of the following is equivalent to $$\sin^2$(x) + \cos^2$(x)$$?

Accepted Answer

$$1$$

Question 15

A zombie virus spreads so that the number of zombies $$Z(t) at $$time $$t (in $$days) is given by $$Z(t) = 100e$$^{0.05t}$$. How long will it take for the number of zombies to reach 405?

Accepted Answer

$$t = \frac{\ln(4.05)}{0.05}$$

Question 16

Given $$f(x) = \log_2$(x-1)$$, what is the domain of $$f$$?

Accepted Answer

$$(1, \infty)$$

Question 17

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

Accepted Answer

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

Question 18

Which of the following is the solution to $$2^{x+1} = 16$?

Accepted Answer

$$x = 3$$

Question 19

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

Accepted Answer

$$25$$

Comprehensive Precalculus Practice Problems and Concepts

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