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:
[tex]2x + y^2 = 6[/tex]
To determine if y is a function of x, we first solve for y
We have:
[tex]2x + y^2 = 6[/tex]
Subtract 2x from both sides
[tex]y^2 = 6 - 2x[/tex]
Square both sides
[tex]y = \±\sqrt{6 - 2x}[/tex]
Split
[tex]y = \sqrt{6 - 2x}[/tex] or [tex]y = -\sqrt{6 - 2x}[/tex]
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
Read more about functions and relations at:
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