# How do you find the domain and range of #g(x) = x/(x^2 - 16)#?

##### 2 Answers

The domain of

The range is

#### Explanation:

As you cannot divide by

Therefore,

The domain of

To calculate the range, proceed as follows

Let

This is a quadratic equation in

the discriminant

Therefore,

The range is

graph{x/(x^2-16) [-10, 10, -5, 5]}

Domain:

Range:

#### Explanation:

Given:

First factor the denominator since

**Find the Domain** - valid input - usually

For most functions, the domain is

- a radical such as a square root - limits the domain
- a denominator - can produce holes and/or vertical asymptotes
- inverse trigonometry functions
- natural log function
#(y = ln x)#

In your example, the vertical asymptotes are the cause. When the denominator function

Domain:

**Find the Range** - valid output - usually

For most functions, the range is also

- a radical such as a square root - limits the range
- a quadratic or even powered function can limit the range. The vertex will be a minimum or a maximum
- absolute value functions can have a vertex
- a rational function (has a numerator and denominator) can have a horizontal asymptote
- a natural exponential function (
#y = e^x# )

In your example, w have a rational function. The degree of the numerator function = 1

Range:

But you can see from the graph below that the point

How would you know this without graphing the function? Create a table of values.

graph{x/(x^2-16) [-10, 10, -5, 5]}