SOLUTION: Find the domain and range for the function. Use interval notation. f(x)= (x^2 + x

SOLUTION: Find the domain and range for the function. Use interval notation. f(x)= (x^2 + x - 12)/[(x-3)(x+5)]

Question 92797: Find the domain and range for the function. Use interval notation.
f(x)= (x^2 + x - 12)/[(x-3)(x+5)]
Answer by mathispowerful(115) (Show Source): You can put this solution on YOUR website!

First simplify it:
factor the numerator. we get
,
cancel the common factor x-3
we get
for a rational expression, the denominator can not be 0,
so x can not equal to -5
the domain is any real number except -5.
The range: Let's simplify further
=
=
let's take a look at the fraction
when x is in the neighborhood of -5, the fraction can be positive infinity and
negative infinity, and thus can be both positive infinity and
negative infinity.
so the range is from negative infinity to positive infinity.
this conclusion can be verified by the graph of below:

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