Skip to content Skip to navigation

Connexions

You are here: Home » Content » Finding the Domain of Simple Rational Functions

Navigation

Content Actions
  • Download module PDF
  • Add to ...
    Add the module to:
    • My Favorites
    • A lens
    • An external social bookmarking service
    • My Favorites (What is '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 (What is 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.

    • External bookmarks
  • E-mail the authors

Recently Viewed

This feature requires Javascript to be enabled.

Finding the Domain of Simple Rational Functions

Module by: Pradnya Bhawalkar, Kim Johnston

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

{x|x≠0}xx0

Exercise 1

Find the domain of y=1x-5 y1x5

Solution 1

{x|x≠5}xx5 since x-5≠0x50, x≠5x5

Exercise 2

Find the domain of y=4x+3x-7 y 4 x 3 x 7

Solution 2

{x|x≠7}xx7 since x-7≠0x70, x≠7x7

Exercise 3

Find the domain of y=7x5-2x y7x52x

Solution 3

{x|x≠52}xx52 since 5-2x≠052x0, x≠52x52

Exercise 4

Find the domain of y=2x-3x+7 y 2 x 3 x 7

Solution 4

{x|x≠3∨-7} x x 3 7 since x≠3 x 3 and x≠-7 x 7

Exercise 5

Find the domain of y=7x2x2-7x+3 y 7 x 2 x 2 7 x 3

Solution 5

{x|x≠12∨3} x x 12 3 since 2x2-7x+3≠0 2 x 2 7 x 3 0 , 2x-1x-3≠0 2x 1 x 3 0 , 2x-1≠0 2x 1 0 and x-3≠0 x 3 0 , x≠12 x 12 and x≠3 x 3

Exercise 6

y=2x+1x+52 y 2 x 1 x 5 2 -1

Solution 6

{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 y x 3 x 2 25 -1

Solution 7

{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 y x 7 x 2 2 -1

Solution 8

{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 9

{x|x≠3}xx3 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 10

{x|x≠-4∨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

Comments, questions, feedback, criticisms?

Send feedback