Q: Which of the following best describes the end behavior of $$f(x) = \dfrac{2x^2$}{x^2$ - 4}$$?

$$f(x) \to 2 as$$ $$x \to \pm\infty$$

Question 1

Which of the following is the correct solution in interval notation for the inequality $$2x^2$$ \geq 8x$$?

Accepted Answer

$$(-\infty,0] \cup [4,\infty)$$

Question 2

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

Accepted Answer

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

Question 3

For the function $$f(x) = \dfrac{1}{x+2}$$, which of the following is the correct domain?

Accepted Answer

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

Question 4

Given $$f(x) = x^2$ - 4$$, what are the $$x-$$intercepts of the graph of $$f$$?

Accepted Answer

$$(2, 0)$$ and $$(-2, 0)$$

Question 5

Which of the following best describes the end behavior of $$f(x) = \dfrac{2x^2$}{x^2$ - 4}$$?

Accepted Answer

$$f(x) 	o 2 as$$ $$x 	o \pm\infty$$

Question 6

Find the inverse of the function $$f(x) = 2x - 4.$$

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x+4}{2}$$

Question 7

Which of the following is the correct solution to the equation $$\log_2$(x) + \log_2$(x-3) = 2$$?

Accepted Answer

$$x = 4$$

Question 8

A ball is thrown upward from the ground with an initial velocity of $$32 ft/s. $$Its height after $$t$$ seconds is given by $$h(t) = -16t^2$ + 32t. At $$what time does the ball hit the ground again?

Accepted Answer

$$t = 2$$ seconds

Question 9

Which of the following is the correct solution to the system of equations: $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$(2, 1)$$

Question 10

Given $$f(x) = \dfrac{1}{x^2$ - 4}$$, which of the following describes all vertical asymptotes?

Accepted Answer

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

Question 11

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

Accepted Answer

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

Question 12

Which of the following is the correct solution to $$\log_3$(x) - 3\log_3$(x-1) = 10$$?

Accepted Answer

$$x = 3$$^{3.25}$$ + 1$$

Question 13

Which of the following is the correct horizontal asymptote for $$f(x) = \dfrac{2x^2$}{x^2$ - 4}$$?

Accepted Answer

$$y = 2$$

Question 14

Given $$f(x) = \dfrac{1}{x+2}$$, what is the $$y-$$intercept of the graph?

Accepted Answer

$$(0, \frac{1}{2})$$

Question 15

Solve for $$x$$: $$x^2 - 5x + 6 = 0$.

Accepted Answer

$$x = 2 or$$ $$x = 3$$

Question 16

Which of the following is the correct solution to $$2x^2 - 3x - 2 = 0$?

Accepted Answer

$$x = 2 or$$ $$x = -\frac{1}{2}$$

Question 17

If $$f(x) = x^2$ - 4$$ and $$g(x) = x + 2$$, what is $$f(g(x))$$?

Accepted Answer

$$x^2 + 4x$

Question 18

Which of the following is the correct solution to $$\dfrac{2x-1}{x+3} = 1$$?

Accepted Answer

$$x = 4$$

Question 19

Given $$f(x) = x^2$ - 4$$, what is the $$y-$$intercept of the graph?

Accepted Answer

$$(0, -4)$$

Question 20

Which of the following is the correct solution to $$\dfrac{1}{x+2} = 2$$?

Accepted Answer

$$x = -1$$

Precalculus Study Guide: Functions, Graphs, Domains, and Equations

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