10/3/22 - Vertical Transformations

Question 1

What is a vertical reflection?

Answer 1

A reflection across the x-axis.

Question 2

If f(x) is a function, then how do we write a vertical reflection of f(x)?

Answer 2

-f(x)

Question 3

How do you graph a vertical reflection?

Answer 3

Pick key points on the graph and multiply their y-coordinates by -1.

Question 4

How do you represent a vertical stretch of a function?

Answer 4

If f is a function and A > 0, then the graph of Af(x) is a vertical stretch.

Question 5

If A > 1, then do the y-values in a vertical stretch get bigger or smaller?

Answer 5

Bigger. They get smaller when 0 < A < 1 in Af(x)

Question 6

How do you graph a vertical stretch Af(x)?

Answer 6

Pick key points on the graph of f(x) and multiply the y-coordinates by A.

Question 7

How do you represent a vertical shift in a function?

Answer 7

f(x) + k, where k is any number

Question 8

In f(x) + k, where k is negative, is the graph shifted up or down?

Answer 8

Down

Question 9

How do you graph a vertical shift f(x) + k?

Answer 9

Pick points on the graph of f(x) and add k to the y-coordinates.

Question 10

How do you graph Af(x) + k?

Answer 10

First, do the vertical stretch, then the vertical shift.

So, multiply the y-coordinates of f(x) by A, then add k.

Question 11

If the graph of f(x) has the point (4, 3), what is the equivalent point on 3f(x) - 2?

Answer 11

(4, 7)