# How do you find the domain and range and intercepts for #H(x) = [(x - 1) (x + 2) (x - 3)]/(x(x - 4)^2)#?

##### 1 Answer

The domain is all Real numbers with

The intercepts are at

The range is all Real numbers.

#### Explanation:

First, the domain: This is where your function (y-values) *can exist*. The idea here is that you *can never have a #0# in the denominator of a fraction*. (You can't divide

*anything*into zero parts.) Set your denominator equal to

So

Solve for the other expression by taking the square root of both sides:

Add

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

If

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.

(*Cool!*)