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Rational Functions - The Whole Thing

Vertical asymptotes:  Set denominator = 0 and solve

x^2 - 25 = 0 ... ( x - 5 )( x + 5 ) = 0 ... x = 5 , x = -5

The lines x = -5 and x = 5

 

4Horizontal asymptote:
 
Look at2x^2 / x^2 = 2

The line y = 2

Now we're ready to graph...  Remember that plotting points is for sissies, so use your brain!

First, let's graph our intercepts and asymptotes on the graph:


intercept ( 0 , -1/5 ) ... no x intercept ... asymptotes at x = -5 , x = 5 and y = 2
 

* Remember that the graph CANNOT cross the y-axis anywhere else and it CANNOT cross the x-axis at all!

Now, we use our brains and our sentences...