Question 1

Which of the following describes the transformation applied to the graph of $$y = f(x) to $$obtain $$y = f(x) + 4$$?

Accepted Answer

Shift the graph 4 units up.

Question 2

Given the function $$y = f(x)$$, what is the result of the transformation $$y = f(x - 3)$$?

Accepted Answer

The graph shifts 3 units to the right.

Question 3

If the graph of $$y = f(x) is $$reflected over the x-axis, which equation represents the new graph?

Accepted Answer

$$y = -f(x)$$

Question 4

Which transformation is represented by $$y = f(-x)$$?

Accepted Answer

Reflection about the y-axis.

Question 5

What is the effect of multiplying a function $$f(x) by a $$constant $$c \u003e 1 to $$get $$y = c \cdot f(x)$$?

Accepted Answer

The graph stretches vertically by a factor of $$c.$$

Question 6

Given $$y = f(2x)$$, what transformation has been applied to the graph of $$y = f(x)$$?

Accepted Answer

The graph is compressed horizontally by a factor of $$\frac{1}{2}.$$

Question 7

Suppose you have the function $$y = \sqrt{x}. If $$you shift the graph 2 units up and 3 units to the left, what is the new equation?

Accepted Answer

$$y = \sqrt{x + 3} + 2$$

Question 8

Which of the following transformations will result in the graph of $$y = f(x)$$ being reflected over the y-axis and then shifted 5 units down?

Accepted Answer

$$y = f(-x) - 5$$

Question 9

If the graph of $$y = f(x) is $$stretched vertically by a factor of 3 and then shifted 4 units down, what is the resulting equation?

Accepted Answer

$$y = 3f(x) - 4$$

Question 10

A medical researcher models the spread of a virus with $$y = f(x). If $$the time axis is rescaled so that each unit represents half as much time, which function models the new situation?

Accepted Answer

$$y = f(2x)$$

Question 11

Given $$y = f(x)$$, which transformation results in $$y = f(x + 5) - 2$$?

Accepted Answer

Shift 5 units to the left and 2 units down.

Question 12

A company models its profit with $$y = f(x). If $$the profit is doubled and the time to reach each profit is halved, what is the new function?

Accepted Answer

$$y = 2f(2x)$$

Question 13

Which of the following transformations will result in the graph of $$y = f(x)$$ being compressed vertically by a factor of $$\frac{1}{3}$$ and shifted 6 units up?

Accepted Answer

$$y = \frac{1}{3}f(x) + 6$$

Question 14

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

Accepted Answer

$$y = -f(x) + 2$$

Question 15

A chemical reaction is modeled by $$y = f(x). If $$the concentration is halved and the reaction time is doubled, what is the new function?

Accepted Answer

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

Question 16

Which transformation is applied to $$y = f(x) to $$obtain $$y = f(-x) + 3$$?

Accepted Answer

Reflect over the y-axis and shift 3 units up.

Question 17

If $$y = f(x) is $$stretched horizontally by a factor of 4, what is the new equation?

Accepted Answer

$$y = f(\frac{1}{4}x)$$

Question 18

A population model is given by $$y = f(x). If $$the population is tripled and the time is shifted 2 units earlier, what is the new function?

Accepted Answer

$$y = 3f(x + 2)$$

Question 19

Which of the following best describes the transformation from $$y = f(x) to$$ $$y = -2f(x - 1) + 5$$?

Accepted Answer

Shift 1 unit to the right, reflect over the x-axis, stretch vertically by a factor of 2, and shift 5 units up.

2.5 Shifting, Reflecting, Stretching, and Compressing Graphs: A Precalculus Study Guide

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