Is x = y^2 a function Step by Step

Step by step

The question

Question: is x = y² a function?

x = y²

A function is a rule where each x has only one y.

One x in, one y out.

function: each x has only one y

1 Draw the graph

Draw the grid.

Draw x = y².

It is a U lying on its side: for each x, y can be the plus or the minus square root.

2 Vertical line test

The vertical line test: draw straight up-and-down lines.

If one of them hits the graph two times, one x has two y's.

Then it is not a function.

Here is a vertical line at x = 4.

It hits the graph two times!

a vertical line with 2 hits → not a function

3 Read the answer

One vertical line hits it more than once.

So it is not a function.

= no, not a function

Careful!

It has a square, like y = x².

But here y is squared.

So one x gives two y's.

Careful: x = y² is not the same as y = x²

4 Check

Let's check with numbers.

x = 4: y squared is 4.

So y is 2 or minus 2.

Two y's, as the line showed.

The same answer!

x = 4: y² = 4 → y = 2 or y = −2

Let's look back.

First: draw the graph.

Then: vertical line test.

Then: read the answer.

Last: check.

Answer