How do you find the domain and range and intercepts for #H(x) = [(x - 1) (x + 2) (x - 3)]/(x(x - 4)^2)#?
The domain is all Real numbers with
The intercepts are at
The range is all Real numbers.
First, the domain: This is where your function (y-values) can exist. The idea here is that you can never have a
Solve for the other expression by taking the square root of both sides:
As far as the intercepts, think about what those are. We often call intercepts "roots" or "zeros" of a function. They are where
Set the numerator
In this case, if any of the three terms in parentheses
Doing the same for the other two terms gives you
Hope that answers your question!
Rational functions (these functions with the expressions in fraction form) are one of only a couple kinds of "basic" functions that don't have an infinite domain.