Asymptotes and Rational Functions

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Presentation transcript:

Asymptotes and Rational Functions Brady Long 4/14/05 4th PPT

The base function The base function is y=1/x Asymptotes are x and y lines that the lines on the graph never touch X=0 and y=0 for the base the asymptotes can vary in position on the graph They are also in different forms

Other forms Asymptotes are also in the form Y=a/(x-h)+k h says how for to move on the x axis h must is opposite because it’s negative says how for to move on the y axis

More forms Asymptotes can also be written in the the form (x+m)/(x-n) for example (x+8)/(x-2) That is also in the correct form But there is a way to find the asymptotes It uses division, addition, and subtraction

How to solve for Asymptotes Watch to see how to solve (-6x+7)/(2x+1) Divide -6x+7 by 2x+1 You get (10)/(2x+1)-3 Multiply top and bottom by ½ You get (5)/(x+.5)-3 The asymptotes h=-.5 and k=-3 graph would be left -.5, down -3

How to find rational function asymptotes We will solve f(x)=(x^2-1)/(2x+5x-12) Factor (x-1)(x+1)/(2x-3)(x+4) Solve equation (2x-3)(x+4)=0 2x-3=0 or x+4=0 X=3/2 or x=-4 This is one way to solve asymptoes

There are way to use computers Also there is graphing Asymptotes are very helpful dealing with different constants