Skip to content Skip to navigation

Connexions

You are here: Home » Content » Transformation of Functions (Graphically)

Navigation

Recently Viewed

This feature requires Javascript to be enabled.

Transformation of Functions (Graphically)

Module by: Debbie Trahan. E-mail the author

User rating (How does the rating system work?)
Ratings

Ratings allow you to judge the quality of modules. If other users have ranked the module then its average rating is displayed below. Ratings are calculated on a scale from one star (Poor) to five stars (Excellent).

How to rate a module

Hover over the star that corresponds to the rating you wish to assign. Click on the star to add your rating. Your rating should be based on the quality of the content. You must have an account and be logged in to rate content.

:
(0 ratings)

Summary: In this module students will apply transformations to the graph of a function.

Note: Your browser may not currently support MathML. See our browser support page for additional details. You can always view the correct math in the PDF version.

The objective of this module is to apply tranformations to the graph of a function.

The graph of the function hx h x is shown in figure 1 . Transfer this graph to your paper. Use the graph of hx h x to help you answer parts a and b for each of the problems 1 - 8.

a. Explain how the given transformation will change the graph of hx h x .

b. Graph the transformation.

Figure 1
Figure 1 (hprob.gif)

Exercise 1

Answer parts a and b for the given transformation. hx−2 h x 2

Solution

The transformation will translate the graph of hx h x 2 units to the right. (figure 2)

Figure 2
Figure 2 (hansa.gif)

Exercise 2

Answer parts a and b for the given transformation. hx−3 h x 3

Solution

The transformation will translate the graph of hx h x 3 units down. (figure 3)

Figure 3
Figure 3 (hansb.gif)

Exercise 3

Answer parts a and b for the given transformation. -hx h x

Solution

The transformation will reflect the graph of hx h x over the x - axis. (figure 4)

Figure 4
Figure 4 (hansc.gif)

Exercise 4

Answer parts a and b for the given transformation. h-x h x

Solution

The transformation reflect the graph of hx h x over the y - axis. (figure 5)

Figure 5
Figure 5 (hansd.gif)

Exercise 5

Answer parts a and b for the given transformation. 2hx 2 h x

Solution

The transformation will vertically stretch the graph of hx h x by a scale factor of 2. (figure 6)

Figure 6
Figure 6 (hanse.gif)

Exercise 6

Answer parts a and b for the given transformation. 12hx 1 2 h x

Solution

The transformation will vertically compress the graph of hx h x by a scale factor of 12 1 2 . (figure 7)

Figure 7
Figure 7 (hansf.gif)

Exercise 7

Answer parts a and b for the given transformation. h2x h 2 x

Solution

The transformation will horizontally compress the graph of hx h x by a scale factor of 12 1 2 . (figure 8)

Figure 8
Figure 8 (hansg.gif)

Exercise 8

Answer parts a and b for the given transformation. h13x h 1 3 x

Solution

The transformation will horizontally stretch the graph of hx h x by a scale factor of 3. (figure 9)

Figure 9
Figure 9 (hansh.gif)

Transformations of Functions Exploration Modules

After you have completed this lesson you can continue to explore transformations of functions by choosing a module listed below.

Go to Transformation of Functions Exploration Module

Go to Transformation of Functions (Verbally) Module

Go to Transformation of Functions using a Graphing Calculator Module

Content actions

Give Feedback:

E-mail the module author | Rate module ( How does the rating system work?)

Rating system

Ratings

Ratings allow you to judge the quality of modules. If other users have ranked the module then its average rating is displayed below. Ratings are calculated on a scale from one star (Poor) to five stars (Excellent).

How to rate a module

Hover over the star that corresponds to the rating you wish to assign. Click on the star to add your rating. Your rating should be based on the quality of the content. You must have an account and be logged in to rate content.

(0 ratings)

Download:

Module PDF

Add module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections directly in Connexions. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need a Connexions account to use 'My Favorites'.

| A lens (?)

Definition of a lens

Lenses

A lens is a custom view of Connexions content. You can think of it as a fancy kind of list that will let you see Connexions through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to Connexions materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual Connexions member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks