SOLUTION: graph the rational function f(x)=x^2/x^2-x-12

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Question 147742: graph the rational function
f(x)=x^2/x^2-x-12
Answer by nabla(475) About Me  (Show Source):
You can put this solution on YOUR website!
First of all, look at the denominator. It factors as (x-4)(x+3).
So, we know that x=4 and x=-3 cannot possibly be valued because they result in division by zero. They are vertical asymptotes. Horizontal asymptote exists at y=1/1 due to the coefficient of the highest degree of the numerator divided by its counterpart in the denominator (squared terms).

Now, f(0)=0/-12=0 is the y-intercept.
f(x)=0 is the x-intercept.
This is, for the most part, all the information you need to produce the following graph (note that you may want to compute values to determine magnitudes of curves for a more accurate graph):
graph%28+300%2C+200%2C+-5%2C+5%2C+-5%2C+5%2C+x%5E2%2F%28x%5E2-x-12%29+%29
Note that the vertical lines that this site draws in do not belong in the picture.