Question

how do you find the domain and range of the rational function f(x) = (-3/(x^2-4)

Answer 1

domain is not too bad, set the denominator \(x^2-4\) equal to zero and solve for \(x\)

Answer 2

that is
solve \(x^2-4=\implies x^2=4\implies x=\pm2\)

Answer 3

as for the ranges, that is a bit harder

Answer 4

you have to solve \(y=\frac{-3}{x^2-4}\) for \(x\) or else graph

Answer 5

unless this is a calculus course. is it?

Answer 6

precalculus

Answer 7

ok here is the cheating way to do it
http://www.wolframalpha.com/input/?i=range++-3%2F%28x^2-4%29

Answer 8

but if you want to do it by hand, you have to solve
\[y=\frac{-3}{x^2-4}\] for \(x\) i don't think there is another way to do it
you get
\[y(x^2-4)+3=0\]
\[yx^2-4y+3=0\]
then use the quadratic formula with \(a=y, b=0, c=-4y+3\) the discriminant is
\[-4y(-4y+3)\] and it has to be positive or there is no solution to the quadratic equation

Answer 9

that is how you get \(y<0\) or \(y>\frac{3}{4}\)