Question 1

Which of the following relations is NOT a function?

Accepted Answer

$$\{(-2, 2), (1, 4), (1, 1), (3, -2)\}$$

Question 2

Given the equation $$x^2$$ + $$y^2 = 25$, is this equation a function? Why or why not?

Accepted Answer

No, because for some $$x$$ values there are two corresponding $$y$$ values.

Question 3

What is the domain of the function $$f(x) = \sqrt{x+4}$$?

Accepted Answer

$$[-4, \infty)$$

Question 4

Which transformation describes the function $$g(x) = -f(x-3) + 2$$?

Accepted Answer

Reflect $$f(x)$$ over the $$x-$$axis, shift right 3 units, then up 2 units.

Question 5

Find the domain of $$f(x) = \frac{1}{x^2$ - 5x + 6}.$$

Accepted Answer

$$(-\infty, 2) \cup (2, 3) \cup (3, \infty)$$

Question 6

Given $$f(x) = x^2$ and g(x$$) = \sqrt{x-8}$$, find (f$$ \circ g)(x)$$ and its domain.

Accepted Answer

$$(f \circ g)(x) = (\sqrt{x-8})^2$ = x-8$$, domain: $$[8, \infty)$$

Question 7

Which of the following best describes the range of $$f(x) = x^2$?

Accepted Answer

$$[0, \infty)$$

Question 8

If $$f(x) = x^2$ + \frac{1}{x}$$ and $$g(x) = x^2$ + x + 2$$, what is the domain of $$f(x) + g(x)$$?

Accepted Answer

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

Question 9

Given $$f(x) = \sqrt{x}$$ and $$g(x) = 3x - 6$$, what is the domain of $$\frac{f(x)}{g(x)}$$?

Accepted Answer

$$[0, 2) \cup (2, \infty)$$

Question 10

Which of the following is the correct composition for $$h(x) = \sqrt{x-2} as$$ $$h(x) = (f \circ g)(x)$$?

Accepted Answer

$$f(x) = \sqrt{x},\ g(x) = x-2$$

Question 11

A function $$f(x) is $$reflected over the $$y-$$axis. Which equation represents this transformation?

Accepted Answer

$$f(-x)$$

Question 12

Given $$f(x) = x^3$ and h(x$$)$$ is f(x$$)$$ reflected over the x$-axis and shifted down 2 units, what is h(x$$)$$?

Accepted Answer

$$h(x) = -x^3$ - 2$$

Question 13

Which of the following is the domain of $$f(x) = \frac{2}{x-5}$$?

Accepted Answer

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

Question 14

If $$f(x) = x^2$ + 3x - 10$$, express $$h(x) = \frac{1}{x^2$ + 3x - 10} as a $$composition $$h(x) = (f \circ g)(x). $$Which is a valid choice for $$g(x)$$?

Accepted Answer

$$g(x) = x^2$ + 3x - 10$$,\ f(x) = \frac{1}{x}$

Question 15

Which of the following is the correct interval notation for the set $$\{x\ |\ -4 \leq x \u003c 5\}$$?

Accepted Answer

$$[-4, 5)$$

Question 16

If $$f(x) = x^2$ and g(x) = x-1$, what is (f$$ \circ g)(3)$$?

Accepted Answer

$$4$$

Question 17

Which of the following is the range of $$f(x) = \sqrt{x}$$?

Accepted Answer

$$[0, \infty)$$

Question 18

Given $$f(x) = x^2$ + 4$$ and $$g(x) = 5x + 7$$, what is $$f(x) + g(x)$$?

Accepted Answer

$$x^2 + 5x + 11$

Study Guide: Functions and Their Graphs (Precalculus, Ch. 3)

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