Question 1

Given $$f(x) = x^2$ - 4x$$ and $$g(x) = \sqrt{x + 4}$$, what is the domain of $$g(x)$$?

Accepted Answer

$$x \geq -4$$

Question 2

For the function $$f(x) = x^2$ - 4x$$, what is the average rate of change between $$x = 5$$ and $$x = 21$$?

Accepted Answer

$$28$$

Question 3

Let $$f(x) = \begin{cases} 4 & 	ext{if } x \leq 2 \ 3x & 	ext{if } x \u003e 2 \end{cases}. $$What is $$f(3)$$?

Accepted Answer

$$9$$

Question 4

Given the quadratic function $$f(x) = -2x^2$ + 8x + 5$$, what is the maximum or minimum value of $$f$$?

Accepted Answer

$$13$$

Question 5

Which of the following is the correct inverse of $$f(x) = x^2$ - 4x$$ for $$x \geq 2$$?

Accepted Answer

Question 6

If $$P(x) = 2x^4$ - 11x^3$ + 10x + 8$$, which of the following is a possible rational zero according to the Rational Root Theorem?

Accepted Answer

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

Question 7

For the function $$r(x) = \frac{3x^2$ + 6x - 7}{x^2$ - 4}$$, what are the vertical asymptotes?

Accepted Answer

$$x = 2$$ and $$x = -2$$

Question 8

A survey finds that the average starting salary for young people is proportional to the square of the number of years of education completed. If a college graduate with 16 years of education has an average starting salary of $48,000, what is the average starting salary for a person who drops out of high school after completing the tenth grade?

Accepted Answer

$$18,750$$

Question 9

If $$y = 120$$ rats are released onto an island and after 15 months there are $$280$$ rats, assuming exponential growth, what is the population after 3 years?

Accepted Answer

$$1,200$$

Question 10

Given $$f(x) = \cos$$^{-1}$$ x$$, what is the domain of $$f$$?

Accepted Answer

$$[-1, 1]$$

Question 11

Find the exact value of $$\log_2$ \left( \frac{\sqrt{2}}{8} \right).$$

Accepted Answer

$$-2.5$$

Question 12

If $$f(x) = x^2$ - 4x$$ and $$g(x) = \sqrt{x + 4}$$, what is $$f(g(8))$$?

Accepted Answer

$$4$$

Question 13

Which graph corresponds to $$k(x) = x^3$ - 3x^2$?

Accepted Answer

Graph D

Question 14

For the trigonometric identity $$8 \sin^2$ 	heta \cos^2$ 	heta = 1 - \cos 4	heta$$, which of the following is true?

Accepted Answer

It is valid for all $$	heta$$

Question 15

If $$P(x) = 2x^4$ - 11x^3$ + 10x + 8$$, which of the following is a root with multiplicity 1?

Accepted Answer

$$x = 1$$

Question 16

Given the Ferris wheel model $$M(t) = 40 \cos \left( \frac{\pi}{30} t \right) + 45$$, what is the height of the wheel after 15 seconds?

Accepted Answer

$$75$$

Question 17

Find the side labeled $$x in $$the triangle with angles $$70^\circ$$, $$65^\circ$$, and side $$5.0$$ opposite $$65^\circ.$$

Accepted Answer

$$5.7$$

Question 18

For the function $$f(x) = -2x^2$ + 8x + 5$$, what is the interval where $$f is $$increasing?

Accepted Answer

Question 19

If $$\cos 2x - \sin x = 0 in $$the interval $$[0, 2\pi)$$, what is one solution?

Accepted Answer

$$x = \frac{\pi}{2}$$

Comprehensive Precalculus Final Exam Review Guidance

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