What is the domain and range of #f(x) =(3x^2-2x-8)/(2x^3+x^2-3x)#?
To find the domain, we have to look for any cases where division by zero can occur. In this case, we have to make sure
Solving we have two options
We have to solve the second equation to get
So the function is undefined at
This means our domain is
As you get closer to any of those x-values we found, the denominator gets closer to 0. As the denominator gets closer to 0, the resulting value goes to positive or negative infinity so the range is