$$\text{All } x \text{-values for which the function is defined}$$

$$\text{A finite set of values}$$

Question 1

Which of the following best describes the domain of a function as shown in the third image (left graph)?

Accepted Answer

$$	ext{All } x 	ext{-values for which the function is defined}$$

Question 2

Given the interval notation $$[-4, 5)$$ for the domain, which of the following is the correct set builder notation?

Accepted Answer

$$\{x\ |\ -4 \leq x \u003c 5\}$$

Question 3

If $$f(x) is $$reflected over the x-axis, which of the following represents the new function?

Accepted Answer

$$-f(x)$$

Question 4

Which transformation is represented by $$f(x-h) + k$$?

Accepted Answer

$$	ext{Shift}$$

Question 5

A function $$f(x) is $$vertically stretched by a factor of 3. Which equation represents this transformation?

Accepted Answer

$$3f(x)$$

Question 6

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

Accepted Answer

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

Question 7

If the domain of $$f(x) is$$ $$[0, 4]$$ and the range is $$[-2, 3]$$, which of the following statements is true?

Accepted Answer

$$f(x) is $$only defined for $$0 \leq x \leq 4$$

Question 8

Which transformation would shift the graph of $$f(x)$$ two units to the right and three units up?

Accepted Answer

$$f(x-2) + 3$$

Question 9

If $$f(x) is $$defined for $$x in$$ $$[-2, 5]$$, what is the domain of $$g(x) = f(x-1)$$?

Accepted Answer

$$[-3, 4]$$

Question 10

A function $$f(x) is $$reflected over the y-axis and then shifted up by 4 units. Which equation represents this transformation?

Accepted Answer

$$f(-x) + 4$$

Question 11

Which of the following best describes the range of a function as shown in the first image (right graph)?

Accepted Answer

$$	ext{A finite set of values}$$

Question 12

If $$f(x) is $$compressed vertically by a factor of $$\frac{1}{2}$$, which equation represents this transformation?

Accepted Answer

$$\frac{1}{2}f(x)$$

Question 13

Which transformation would reflect $$f(x)$$ over the y-axis?

Accepted Answer

$$f(-x)$$

Question 14

If $$f(x)$$ has domain $$[1, 6]$$ and range $$[0, 5]$$, what is the range of $$g(x) = -f(x)$$?

Accepted Answer

$$[-5, 0]$$

Study Guide: Functions and Their Graphs (Precalculus Chapter 1)

Study Guide - Practice Questions