Question 1

Which of the following best describes a function?

Accepted Answer

A relation where each input has at most one output.

Question 2

Given the relation $$\{(-3, 5), (0, 2), (3, 5)\}$$, what are the inputs and outputs, and is this a function?

Accepted Answer

Inputs: $$\{-3, 0, 3\}$$, Outputs: $$\{2, 5\}$$, Yes, it is a function.

Question 3

Which equation below is NOT a function?

Accepted Answer

$$x^2$$ + $$y^2 = 25$

Question 4

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

Accepted Answer

$$[0, \infty)$$

Question 5

Given $$f(x) = \frac{2}{x-5}$$, what is the domain of $$f(x)$$?

Accepted Answer

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

Question 6

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

Accepted Answer

$$(f \circ g)(x) = (x - 1)^2$

Question 7

Which transformation is represented by $$f(x) \rightarrow f(x-3) + 2$$?

Accepted Answer

Shift right 3 units and up 2 units.

Question 8

What is the effect of the transformation $$g(x) = -f(x) on $$the graph of $$f(x)$$?

Accepted Answer

Reflection over the x-axis.

Question 9

Given $$f(x) = x^2$ and g(x$$) = \sqrt{x-8}$$, what is the domain of (f$$ \circ g)(x)$$?

Accepted Answer

$$[8, \infty)$$

Question 10

If $$f(x) = |x|$$, what is the equation for the function reflected over the y-axis and shifted up 2 units?

Accepted Answer

$$g(x) = | -x | + 2$$

Question 11

Given $$f(x) = x^2$ and g(x) = x + 4$, find (f + g)(x$$)$$ and its domain.

Accepted Answer

$$(f + g)(x) = x^2$ + x + 4$$, domain: $$(-\infty, \infty)$$

Question 12

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

Accepted Answer

$$[-4, 5)$$

Question 13

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

Accepted Answer

$$[-4, \infty)$$

Question 14

Which transformation results in a vertical stretch of a function by a factor of 3?

Accepted Answer

$$g(x) = 3f(x)$$

Question 15

Given $$f(x) = x^2$ and g(x) = x + 2$, what is (g$$ \circ f)(x)$$?

Accepted Answer

$$(g \circ f)(x) = x^2$ + 2$$

Question 16

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

Accepted Answer

$$[0, \infty) \setminus \{\sqrt{2} - 2\}$$

Question 17

Which of the following is the correct set builder notation for the range $$[-1, 2)$$?

Accepted Answer

$$\{y | -1 \leq y \u003c 2\}$$

Question 18

If $$f(x) = x^3$ is reflected over the x-axis and then shifted down 2 units, what is the equation for the new function h(x$$)$$?

Accepted Answer

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

Question 19

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

Accepted Answer

$$[2, \infty)$$

Functions and Their Graphs: Domain, Range, and Transformations

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