Question

Determine whether the relation represents y as a function of x.

Answer 1

It isn’t a function because when you put a value for x you can get two possible answer because the y is being squared

Answer 2

All functions are relations, but not all relations can be said to be a function.

The relation y is not a function of x

Given that:

$2x + y^2 = 6$

To determine if y is a function of x, we first solve for y

We have:

$2x + y^2 = 6$

Subtract 2x from both sides

$y^2 = 6 - 2x$

Square both sides

$y = \±\sqrt{6 - 2x}$

Split

$y = \sqrt{6 - 2x}$ or $y = -\sqrt{6 - 2x}$

This means that:

For one value of x, there are two possible values of y

This scenario is regarded as a one-to-many relation.

This type of relation is not a function.

Hence, y is not a function of x

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