Question 1

Which of the following is the domain of the function $$f(x) = \frac{1}{x+5}$$?

Accepted Answer

$$(-\infty, -5) \cup (-5, \infty)$$

Question 2

What is the horizontal asymptote of the function $$y = \frac{4}{5x-1} - 5$$?

Accepted Answer

$$y = -5$$

Question 3

For the function $$h(x) = \sqrt{16-x^2$}$$, what is the domain?

Accepted Answer

$$[-4, 4]$$

Question 4

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

Accepted Answer

$$[1, \infty)$$

Question 5

What is the period of the function $$y = 4\sin(2\pi x)$$?

Accepted Answer

$$1$$

Question 6

Which of the following is the equation of the vertical asymptote for $$y = 2\log(x-1)$$?

Accepted Answer

$$x = 1$$

Question 7

What is the amplitude of $$y = 3\cos\left(\frac{3}{2}\pi x\right)$$?

Accepted Answer

$$3$$

Question 8

Solve for $$x in $$the equation $$\ln(4x) = 1.$$

Accepted Answer

$$x = \frac{e}{4}$$

Question 9

What is the difference quotient for $$f(x) = 3x^2$ + 5x - 6$$?

Accepted Answer

$$\frac{3[(x+h)^2$ - x^2$] + 5h}{h}$$

Question 10

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

Accepted Answer

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

Question 11

Convert the polar coordinates $$(3, \frac{\pi}{4}) to $$rectangular coordinates.

Accepted Answer

$$(\frac{3\sqrt{2}}{2}, \frac{3\sqrt{2}}{2})$$

Question 12

If $$f(x) = x^3$ - 6x^2$ + 11x - 6$$, what are the zeros of $$f(x)$$?

Accepted Answer

$$x = 1, 2, 3$$

Question 13

Which of the following is the simplified form of $$\frac{3a^2$b}{ab}$$?

Accepted Answer

$$3a$$

Question 14

Solve the inequality $$x^2 - x - 2$$ \u003c 0$$.

Accepted Answer

$$(-1, 2)$$

Question 15

What is the value of $$\sin\left(\frac{\pi}{6}\right)$$?

Accepted Answer

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

Question 16

Given the function $$f(x) = 	an$$^{-1}$$(x)$$, what is the range?

Accepted Answer

$$\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$$

Question 17

What is the solution to $$\cos(2x) + 1 = 0$$ for $$0 \leq x \u003c 2\pi$$?

Accepted Answer

$$x = \frac{\pi}{2}, \frac{3\pi}{2}$$

Question 18

Which of the following is the simplified form of $$\left(\frac{2y^4$}{3y^5$}\$$right)^2$$?

Accepted Answer

$$\frac{4}{9y^2$}$$

Question 19

What is the period of $$y = 2	an(4\pi x)$$?

Accepted Answer

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

Question 20

Given the graph in $$image_2$$, what is the absolute maximum value of the function?

Accepted Answer

$$y = 5 at$$ $$x = 4$$

Analyzing Absolute and Local Extrema from Graphs

Study Guide - Practice Questions