There are three types of rational functions. Type 1 has a horizontal asymptote of y=0. The vertical asymptote is where the bottom equals 0. Type 2 has the same power in the numerator and denominator, so the horizontal asymptote equals a number other than zero. Type 3 has a higher power in the numerator than the denominator. To solve any type, you must find the vertical and horizontal asymptotes, x-intercepts, y-intercepts, domain and range, and create a table and graph.

1. Rational FunctionsHow to solve different types.

2. Rational fucntion:Has a function in the numerator and denominator. There are three different types of rational functions.

3. Type 1The horizontal asymptote (HA) will always equal zero when the expression is type 1. In order to solve a type 1 you must find the following:Vertical Asymptote (VA): bottom equal to 0Horizontal Asymptote (HA): y=0 every timeX-intercept: top equation equal to 0. Y=0Y-intercept: Use the table on calculator. X=0Domain: ( )( )Range: ( )( )And a table and a graph.

4. Type 1 exampleWhen the power of the denominator is bigger than numerator.Y= 6x+8 (x-1)(x-3)VA: x=1, x=(-3) HA: y=0 X-int: y=0 6x+8=0 -8 -86x = -8 6 6X= -1.33 Table Y-int: x=0 (0, -2.67) Graph

5. Type 2When the power of the numerator and denominator are the same.Y= a number this time it’s not just zero like type 1. Example: y= x+4 x-1 VA: x=1HA: y=1X-int: y=0 (-4,0)X+4 =0 -4 -4X= -4Y-int: x=0 (-4,0)

6. Type 3When the power of the numerator is bigger than the denominator.Example: