Skip to content Skip to navigation Skip to collection information

OpenStax_CNX

You are here: Home » Content » Advanced Algebra II: Activities and Homework » Homework: Horizontal and Vertical Permutations I

Navigation

Table of Contents

Lenses

What is a lens?

Definition of a lens

Lenses

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

What is in a lens?

Lens makers point to 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 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.

This content is ...

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • Featured Content display tagshide tags

    This collection is included inLens: Connexions Featured Content
    By: Connexions

    Comments:

    "This is the "main" book in Kenny Felder's "Advanced Algebra II" series. This text was created with a focus on 'doing' and 'understanding' algebra concepts rather than simply hearing about them in […]"

    Click the "Featured Content" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Also in these lenses

  • Busbee's Math Materials display tagshide tags

    This collection is included inLens: Busbee's Math Materials Lens
    By: Kenneth Leroy Busbee

    Click the "Busbee's Math Materials" link to see all content selected in this lens.

    Click the tag icon tag icon to display tags associated with this content.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
 

Homework: Horizontal and Vertical Permutations I

Module by: Kenny M. Felder. E-mail the author

Summary: This module provides practice problems designed to develop some concepts related to horizontal and vertical permutations of functions by graphing.

  1. One way of expressing a function is with a table. The following table defines the function f ( x ) f(x).
Table 1
x 0 1 2 3
f ( x ) f(x) 1 2 4 8
  1. f ( 2 ) = f(2)=
  2. f ( 3 ) = f(3)=
  3. f ( 4 ) = f(4)=

Now, I’m going to define a new function this way: g ( x ) = f ( x ) −2 g(x)=f(x)−2. Think of this as a set of instructions, as follows: Whatever number you are given, plug that number into f ( x ) f(x), and then subtract two from the answer.

  1. g ( 2 ) = g(2)=
  2. g ( 3 ) = g(3)=
  3. g ( 4 ) = g(4)=

Now, I’m going to define yet another function: h ( x ) = f ( x 2 ) h(x)=f(x2). Think of this as a set of instructions, as follows: Whatever number you are given, subtract two. Then, plug that number into f ( x ) f(x).

  1. h(2)=
  2. h(3)=
  3. h(4)=
  4. Graph all three functions below. Label them clearly so I can tell which is which!
  1. Standing at the edge of the Bottomless Pit of Despair, you kick a rock off the ledge and it falls into the pit. The height of the rock is given by the function h ( t ) = –16 t 2 h(t)=–16 t 2 , where t is the time since you dropped the rock, and h h is the height of the rock.
  1. Fill in the following table.
Table 2
time (seconds) 0 ½ 1 2 3
height (feet)                
  1. h ( 0 ) = 0 h(0)=0. What does that tell us about the rock?
  2. All the other heights are negative: what does that tell us about the rock?
  3. Graph the function h ( t ) h(t). Be sure to carefully label your axes!
Figure 1: h ( t ) = 16 t 2 h(t)=16 t 2
Figure 1 (fig3.png)
  1. Another rock was dropped at the exact same time as the first rock; but instead of being kicked from the ground, it was dropped from your hand, 3 feet up. So, as they fall, the second rock is always three feet higher than the first rock.
  1. Fill in the following table for the second rock.
Table 3
time (seconds) 0 ½ 1 2 3
height (feet)                
  1. Graph the function h ( t ) h(t) for the new rock. Be sure to carefully label your axes!
Figure 2
Figure 2 (fig2.png)
  1. How does this new function h ( t ) h(t) compare to the old one? That is, if you put them side by side, what change would you see?
  2. The original function was h ( t ) = –16 t 2 h(t)=–16 t 2 . What is the new function?
    h ( t ) = h(t)=
    (*make sure the function you write actually generates the points in your table!)
  3. Does this represent a horizontal permutation or a vertical permutation?
  4. Write a generalization based on this example, of the form: when you do such-and-such to a function, the graph changes in such-and-such a way.
  1. A third rock was dropped from the exact same place as the first rock (kicked off the ledge), but it was dropped 1½ seconds later, and began its fall (at h = 0 h=0) at that time.
  1. Fill in the following table for the third rock.
Table 4
time (seconds) 0 ½ 1 2 3 4 5
height (feet) 0 0 0 0              
  1. Graph the function h ( t ) h(t) for the new rock. Be sure to carefully label your axes!
Figure 3
Figure 3 (fig1.png)
  1. How does this new function h ( t ) h(t) compare to the original one? That is, if you put them side by side, what change would you see?
  2. The original function was h ( t ) = –16 t 2 h(t)=–16 t 2 . What is the new function?
    h ( t ) = h(t)=
    (*make sure the function you write actually generates the points in your table!)
  3. Does this represent a horizontal permutation or a vertical permutation?

Write a generalization based on this example, of the form: when you do such-and-such to a function, the graph changes in such-and-such a way.

Collection Navigation

Content actions

Download:

Collection as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add:

Collection to:

My Favorites (?)

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

| A lens I own (?)

Definition of a lens

Lenses

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

What is in a lens?

Lens makers point to 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 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

Module to:

My Favorites (?)

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

| A lens I own (?)

Definition of a lens

Lenses

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

What is in a lens?

Lens makers point to 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 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