SOLUTION: Which graph represents the function of f(x) = the quantity of 9 x squared plus 9 x minus 18, all over 3 x plus 6

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Question 892246: Which graph represents the function of f(x) = the quantity of 9 x squared plus 9 x minus 18, all over 3 x plus 6
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = the quantity of 9 x squared plus 9 x minus 18, all over 3 x plus 6
One may guess that you have f%28x%29=%289x%5E2%2B9x-18%29%2F%283x%2B6%29 which should be simplified.
f%28x%29=%289%2F3%29%28%28x%5E2%2Bx-2%29%2F%28x%2B2%29%29
highlight%28f%28x%29=3%28%28%28x%2B2%29%28x-1%29%29%2F%28x%2B2%29%29%29

This will have a HOLE at x=-2, although seeing it on the graph on the site will be difficult
or impossible. A zero occurs at x=1. As x goes increasingly large or small (tend toward pos or neg
infinity), f approaches y=3%28x-1%29=3x-3. Critical values of x are -2 and 1, so the signs in
the three intervals should be examined.

graph%28300%2C300%2C-6%2C6%2C-10%2C10%2C3%28%28x%5E2%2Bx-2%29%2F%28x%2B2%29%29%29
Be aware again, a hole occurs at x=-2, f being undefined there.