SOLUTION: What would the range and domain be for the function f(x)=(x+2)/(x^2-9)? Also, for the range would you be able to say all real numbers since the function does cross over the horizo

Question 716457: What would the range and domain be for the function f(x)=(x+2)/(x^2-9)?
Also, for the range would you be able to say all real numbers since the function does cross over the horizontal asymptote?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
has the graph

THE DOMAIN:
That function does not exist when
because we cannot divide by zero.
happens when and when .
Those two values of are not part of the domain.
Other than that,
the function works and gives a value of to
every other real number .
NOTE:
You may be expected to use certain symbols and notation to state the domain.
Maybe you are expected to use set builder notation, such as
{real | and } or something like that.
Or maybe you are expected to use interval notation, as in
(infinite,-3)U(-3,3)U(3,infinite)

THE RANGE:
The denominator has zeros at and ,
but the numerator is not zero at those points,
so the function has vertical asymptotes at and .
The function increases in absolute value without bounds as you approach and .
It is negative on one side and positive on the other,
so it ranges from -infinity to infinity.
It does not just cross over the horizontal asymptote; it keeps going through all the real numbers, positive and negative
Its range is all the real numbers.

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