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

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

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

$$f(x) \\to \infty as$$ $$x \\to \infty$$ and $$f(x) \\to \infty as$$ $$x \\to -\infty$$

Q: Given $$f(x) = \\sqrt{x-2}$$ and $$g(x) = x^2$, find the domain of f(g(x$$))$$.

$$(-\infty,-\sqrt{2}] \\cup [\sqrt{2},\infty)$$

Q: Which of the following is the correct interval notation for the solution to $$x^2 - 5x + 4$$ \u003e 0$$?

$$(-\infty,1) \\cup (4,\infty)$$

Question 1

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

Accepted Answer

$$[-2,2]$$

Question 2

Given $$f(x) = \sqrt{x-2}$$, what is the domain of $$f in $$interval notation?

Accepted Answer

$$[2,\infty)$$

Question 3

If $$f(x) = x^2$ and g(x) = x+2$, what is the domain of f(g(x$$))$$?

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

Find the vertical asymptote of $$f(x) = \frac{1}{x-2}.$$

Accepted Answer

$$x = 2$$

Question 7

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

Accepted Answer

$$f(x) \to \infty as$$ $$x \to \infty$$ and $$f(x) \to \infty as$$ $$x \to -\infty$$

Question 8

Solve for $$x$$: $$2x^2 - 5x - 16 = 0$.

Accepted Answer

$$x = 4, x = -2 ($$distinct roots)

Question 9

Given $$f(x) = \sqrt{x-2}$$ and $$g(x) = x^2$, find the domain of f(g(x$$))$$.

Accepted Answer

$$(-\infty,-\sqrt{2}] \cup [\sqrt{2},\infty)$$

Question 10

Which of the following is the correct solution for $$\log_3$(x^2) - 3$$\$$log_3(x) = 10$?

Accepted Answer

$$x = 3$$^{3.5}$$ and x$$ = $$3^{-2.5}$$

Question 11

For the function $$f(x) = \frac{1}{x+2}$$, what is the $$y-$$intercept?

Accepted Answer

$$(0,1/2)$$

Question 12

Which of the following is the correct interval notation for the solution to $$x^2 - 5x + 4$$ \u003e 0$$?

Accepted Answer

$$(-\infty,1) \cup (4,\infty)$$

Question 13

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

Accepted Answer

$$(0,-4)$$

Question 14

Which of the following is the correct solution for $$x^2 + 5x - 16 = 0$?

Accepted Answer

$$x = -8, x = 2$$

Question 15

For the function $$f(x) = x^2$ - 4$$, which of the following describes the axis of symmetry?

Accepted Answer

$$x = 0$$

Question 16

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

Accepted Answer

$$(0,-4)$$

Question 17

Which of the following is the correct solution for $$x^2 - 5x + 4 = 0$?

Accepted Answer

$$x = 1, x = 4$$

Question 18

For the function $$f(x) = \frac{1}{x+2}$$, what is the horizontal asymptote?

Accepted Answer

$$y = 0$$

Question 19

Which of the following is the correct solution for $$x^2 - 5x + 4$$ \u003c 0$$?

Accepted Answer

$$(1,4)$$

Question 20

Given $$f(x) = x^2$ - 4$$, which of the following is the correct factorization?

Accepted Answer

$$(x-2)(x+2)$$

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

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