What is the graph of the function f(x)=x2+4x−12x+6?

1 Answer
Zor Shekhtman
Jul 10, 2016

Same as y=x−2, except a point x=−6, where function is undefined.

Explanation:

graph{(x^2 +4x -12)/(x+6) [-10, 10, -10, 10]}

Obviously, the function is undefined at x=−6 since its denominator would be equal to zero in this case.

In all other cases we can do a simple transformation:
Since x2+4x−12=(x+6)(x−2),
x2+4x−12x+6=x−2
for all x≠−6

Therefore, our graph would be identical to the one of y=x−2, except in one point x=−6, where function is undefined, and which should be excluded from the graph.

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