Skip to content Skip to navigation Skip to collection information

Connexions

You are here: Home » Content » "Rational"ity » Simple Rational Functions

Navigation

Recently Viewed

This feature requires Javascript to be enabled.
 

Simple Rational Functions

Module by: Pradnya Bhawalkar, Kim Johnston. E-mail the authors

Summary: Finding the domain of rational functions with no other complications such as roots/radicals.

For fractions, the denominator (the bottom) of the fraction cannot equal 00. Determine domain restrictions by setting the denominator equal to 00 and solving.

Example 1

Find the domain of y=1x y1x

xx≠0xx0

Exercise 1

Find the domain of y=1x−5 y1x5

Solution

xx≠5xx5 since x−5≠0x50, x≠5x5

Exercise 2

Find the domain of y=4⁢x+3x−7 y 4 x 3 x 7

Solution

xx≠7xx7 since x−7≠0x70, x≠7x7

Exercise 3

Find the domain of y=7⁢x5−2⁢x y7x52x

Solution

xx≠52xx52 since 5−2⁢x≠052x0, x≠52x52

Exercise 4

Find the domain of y=2(x−3)⁢(x+7) y 2 x 3 x 7

Solution

x x≠3 or −7 x x 3 7 since x≠3 x 3 and x≠−7 x 7

Exercise 5

Find the domain of y=7⁢x2⁢x2−7⁢x+3 y 7 x 2 x 2 7 x 3

Solution

x x≠12 or 3 x x 12 3 since 2⁢x2−7⁢x+3≠0 2 x 2 7 x 3 0 , (2⁢x−1)⁢(x−3)≠0 2x 1 x 3 0 , 2⁢x−1≠0 2x 1 0 and x−3≠0 x 3 0 , x≠12 x 12 and x≠3 x 3

Exercise 6

y=2⁢x+1x+52-1 y 2 x 1 x 5 2 -1

Solution

x x≠−5 x x 5 since x+52≠0 x5 2 0 , x+5≠0 x5 0 , x≠−5 x 5

Exercise 7

Find the domain of y=x+3x2+25-1 y x 3 x 2 25 -1

Solution

x x∈R x x since x2+25≠0 x 2 25 0 , x2≠−25 x2 25 , x∈R x

Exercise 8

Find the domain of y=x−7x2+2-1 y x 7 x 2 2 -1

Solution

x x∈R x x since x2+2≠0 x 2 2 0 , x2≠−2 x2 2 , x∈R x

Exercise 9

Find the domain of y=5|x−3| y 5 x3

Solution

xx≠3xx3 since |x−3|≠0 x3 0 , x−3≠0 x3 0 , x≠3 x 3

Exercise 10

Find the domain of y=4|x|−4 y 4 x 4

Solution

x x≠−4 or 4 x x 4 4 since |x|−4≠0 x 4 0 , |x|≠4 x 4 , x≠-4 x -4 and x≠4 x 4

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