SOLUTION: What is the graph of the rational function? y= x^2-7x+12/x^2-1

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Question 887756: What is the graph of the rational function?
y= x^2-7x+12/x^2-1
Found 2 solutions by jim_thompson5910, josgarithmetic:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Use a graphing calculator to get


Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
The graph of y= x^2-7x+12/x^2-1 is this:

graph%28300%2C300%2C-25%2C25%2C-15%2C40%2Cx%5E2-7x%2B12%2Fx%5E2-1%29

But that is not what you want.

You want this:
y= (x^2-7x+12)/(x^2-1)
y=+%28x%5E2-7x%2B12%29%2F%28x%5E2-1%29
-
That seems not factorable to simplify, but there is still some information to learn about the graph if factor the function.
y=%28%28x-3%29%28x-4%29%29%2F%28%28x-1%29%28x%2B1%29%29
Zeros at x=3 and x=4.
Asymtptotes (vertical) at x=1 and x=-1.
You can test the intervals around all critical points...

THIS is the graph. (Difficult for this to appear well on the system)
graph%28400%2C400%2C-15%2C15%2C-15%2C15%2C%28x%5E2-7x%2B12%29%2F%28x%5E2-1%29%29

A zoom-in on the right side
graph%28300%2C300%2C2%2C5%2C-1%2C1%2C%28x%5E2-7x%2B12%29%2F%28x%5E2-1%29%29