How do you decide whether the relation x = y² defines a function?

Nov 15, 2017

We can graph the relation and do the vertical line test.

Explanation:

Whenever we have to check if a relation is a function, we draw its graph and do the vertical line test.

The vertical line test says that if a vertical line touches the graph once, the relation is a function. And if the vertical line touches the graph more than once it's not a function.

Example $\to$

$x = {y}^{2}$

$\sqrt{x} = y$

$y = \sqrt{x}$

Let's graph this relation.

graph{sqrtx [-10, 10, -5, 5]}

Now if we draw a vertical line we can see that the line touches the graph at only one point everywhere.

Therefore it is a function.

Additional $\textcolor{red}{\to}$Circles, Ellipses, Hyperbolas etc. are not functions because they don't pass the vertical line test.
A Line, Parabola etc. are functions because they pass the vertical line test.