SOLUTION: f(x)=3x-2/x^2-x-12

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Question 890206: f(x)=3x-2/x^2-x-12
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
It should be written, f(x)=3x-2/x^2-x-12;

highlight_green%28f%28x%29=%283x-2%29%2F%28x%5E2-x-12%29%29.

What do you want from it?

The denominator is factorable.
f%28x%29=%283x-2%29%2F%28%28x%2B3%29%28x-4%29%29

The function has a root (zero) at x=2%2F3 and vertical asymptotes for x=-3 and x=4. You can check intervals between the critical values to find signs in those intervals to get a better idea of the shape of the graph.

graph%28300%2C300%2C-12%2C12%2C-12%2C12%2C%283x-2%29%2F%28x%5E2-x-12%29%29