# How do you find the domain and range and determine whether the relation is a function given :#x=2y^2-3#?

##### 1 Answer

See below.

#### Explanation:

For y as a function of x.

Rearrange;

Add 3 to both sides:

Divide by 2:

Taking roots of both sides:

For positive root:

For the domain we must make sure the numerator is

The numerator is

So the domain is

The range for the positive root is:

As

So the range is:

For negative root the domain is the same for real numbers. The range is in the reverse direction:

The determination of a function.

For positive root only a function is defined.

For negative root only a function is defined.

For

This is not a function. A function is only defined if an element in a domain is mapped onto one and one only element in a range. In the case of both roots this would map one element in the domain to two elements in the range. This is sometimes called a one to many relationship.

See graph: