This section is a review of College Algebra/Precalculus.
The Horizontal Line Test says that if you can draw horizontal lines everywhere through a graph and have no line touch the graph in more than one point, then the graph represents a one-to-one function. However, if you can find so much as one horizontal line that intersects the graph in more than one point, then the graph fails the horizontal line test. Do not confuse this test with the Vertical line test which is used to determine whether or not a graph represents a function.
The following three statements are equivalent:
1. f passes
the horizontal line test.
2. f is a one-to-one function.
3. f has an inverse.
The
following three statements are equivalent:
1. f fails the horizontal line test.
2.
f is not a one-to-one function.
3. f does not have an inverse.
FIU has online movies to help with inverse functions on this page. You must have QuickTime Player, a free download, installed on your computer.
The University of Idaho provides
another online resource. These lectures are only viewable by those with DSL or
cable modems. Real Player, a
free download, is required to see these videos. The videos cover the topics
below. To see the videos, go to this
page and look under section 6.2.
The definition of one-to-one functions,
the horizontal line test and some examples
The domain and range of 1-to-1 functions
and inverse functions and some examples
Verifying that two functions are inverses
of each other
Finding an inverse function
The
definition of the inverse sine function
The
definition of the inverse cosine function
The
definition of the inverse tangent function
Expressions
involving inverse functions values
The Math Emporium at Virginia Tech
has online videos. QuickTime Player, a free
download, is required to view them.
Inverse
Functions
Joliet Junior College has online videos that require Windows
Media Player, a
free download.
Determine
whether a function is one-to-one
Determine
the inverse of a function defined by a map or ordered pair
Obtain
the graph of the inverse function from the graph of the function
More
Online Help:
Inverse
functions at PurpleMath
Inverse
functions at SOS Math
An
Interactive tutorial on inverse functions
Inverse trig functions at TheMathPage.com