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Graphs-of-Rational-Functions

Page history last edited by Kristen Fouss 15 years, 3 months ago

How do you graph a rational function? You have to follow the simple 6-step method of Graphing Rational Functions:

1. Find y-intercept.

2. Find x-intercept.

3. Find Vertical Asymptote.

4. Find Horizontal Asymptote.

5. Plot some points.

6. Graph.

This all looks confusing, so lets go through step by step with an example.

ex. f(x)= 5x+4

1.) Find the y-intercept.

To find the y-intercept, you put 0 in for x, then solve. so....

(5(0)+4)/3(0)=0

4/0=0

0=0....This shows you that there is no y-intercept.

2.) Find the x-intercept.

To find the x-intercept, you set the numerator equal to zero, then solve. so...

5x+4=0

5x=-4

x=-4/5......this shows you have an x-intercept at (-4/5, 0)

3.) Find the vertical asymptote.

To find the vertical aymptote, you set the denominator equal to zero. so...

3x=0

x=0.....this shows you that the line x=0, their is a vertical asymptote.

4.) Find the horizontal asymptote.

To find the horizontal asymptote, you look at the powers on the x's on top and below. If the x on top has a higher power than the x on the bottom, there is NO horizontal asymptote. If the x on top has a lower power than the x on the bottom, the H.A. is y=0. If the two powers are equal, you take the coefficent in front of the x's and divide them.

For example, in our equation the powers are equal, so you take 5/3 to get a H.A. of y=5/3.

5.) Plot some points.

Graph what asymptotes you found, and make a table of x and y values, and plot those points.

6.) Graph

Graph your rational function.

This is another example of a Rational Function