How do you graph a rational function? You have to follow the simple 6step method of Graphing Rational Functions:
1. Find yintercept.
2. Find xintercept.
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
3x
1.) Find the yintercept.
To find the yintercept, 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 yintercept.
2.) Find the xintercept.
To find the xintercept, you set the numerator equal to zero, then solve. so...
5x+4=0
5x=4
x=4/5......this shows you have an xintercept 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
This is how Cliff Notes explains it.
This is another good referance on graphing Rational Functions!!

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