Question 1

Which of the following is the domain of the function $$f(x) = \sqrt{3x - 5}$$?

Accepted Answer

$$x \geq \frac{5}{3}$$

Question 2

Given $$f(x) = \frac{2x^2$ + 1}{x^2$ - 9}$$, what is the equation of the vertical asymptotes?

Accepted Answer

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

Question 3

What is the range of the function $$f(x) = \frac{1}{x-4}$$?

Accepted Answer

$$(-\infty, 0) \cup (0, \infty)$$

Question 4

Find the zeros of the polynomial $$f(x) = x^3$ - 4x^2$ + 4x.$$

Accepted Answer

$$x = 0, 2, 2$$

Question 5

Which of the following describes the horizontal asymptote of $$f(x) = \frac{2x^2$ + 1}{x^2$ - 9}$$?

Accepted Answer

$$y = 2$$

Question 6

If $$f(x) = \sqrt{x^2$ - 5x + 6}$$, what is the domain of $$f$$?

Accepted Answer

$$x \leq 2 or$$ $$x \geq 3$$

Question 7

Given $$f(x) = 2x^2$ - 3x + 1$$, what is the vertex of the parabola?

Accepted Answer

$$(\frac{3}{4}, -\frac{1}{8})$$

Question 8

Which of the following is the inverse of $$f(x) = 3x - 5$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x + 5}{3}$$

Question 9

Solve for $$x$$: $$\log_2$(x - 1) = 3.$$

Accepted Answer

$$x = 9$$

Question 10

Which of the following is the correct transformation for $$f(x) = x^2$ to g(x) = (x$$ - $$2)^2 + 3$?

Accepted Answer

Shift right 2 units and up 3 units

Question 11

What is the solution to $$2\sin x = 1$$ for $$x in$$ $$[0, 2\pi]$$?

Accepted Answer

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

Question 12

Which of the following is the correct polar to rectangular conversion for $$(2, \frac{\pi}{3})$$?

Accepted Answer

$$(1, \sqrt{3})$$

Question 13

What is the solution to $$	an x = 0$$ for $$x in$$ $$[0, 2\pi]$$?

Accepted Answer

$$x = 0, \pi$$

Question 14

Which of the following is the correct simplification of $$\frac{a^7$}{a^3$}$$?

Accepted Answer

$$a^4$$

Question 15

If $$f(x) = \frac{1}{x}$$, which of the following is the correct difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$\frac{-h}{x(x+h)}$$

Question 16

Which of the following is the correct identity for $$\sin^2$ x + \cos^2$ x$$?

Accepted Answer

$$1$$

Question 17

What is the solution to $$\log_3$(x) = 2$$?

Accepted Answer

$$x = 9$$

Question 18

Which of the following is the correct equation for the graph of a circle with center $$(2, -3)$$ and radius $$4$$?

Accepted Answer

$$(x - 2)^2$ + (y + 3)^2$ = 16$$

Question 19

Which of the following is the correct solution to $$2x^2 - 5x + 2 = 0$?

Accepted Answer

$$x = 2, x = \frac{1}{2}$$

Precalculus Final Exam Review – Comprehensive Study Notes

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