Sept. 26 Class

New Unit: Rational Functions

A rational function is any function that has a numerator and denominator, (ie. a fraction).

For example: .

We know that the denominator can never be zero, therefore we must state the restriction, x ≠ 0.

We can state the restrictions to any rational function by making sure the denominator does not equal zero.

Example: State the restrictions to .

Solution:  (x – 4)(3x + 2) ≠ 0, therefore, x ≠ 4 and x ≠ -2/3.


Rational expressions can be simplified if you have the same factor in the numerator and denominator.  Make sure to factor!

Example: Simplify and state the restrictions, .

Solutions: First we must factor to get, .  Now we see the same factor of x in the numerator and denominator.  Those "cancel out", leaving (2x + 1).  Note that even though the factor of x has been eliminated, the restriction still holds,

x ≠ 0

On a graph of this expression, you would find a hole at the restricted point.

It is very important that you state the restrictions from the original expression, before you simplify.

Example: Simplify and state the restrictions.

Solutions: First we must factor to get, . 

The restrictions are then x ≠ 3 and x ≠ -3.

Now we can simplify to get, .

Homework:  

Pg. 112  #1-11, 15

Pg. 107 #1eoo, 7, 8

Read, understand, and make notes: Pg. 116 (In summary)