Is y = -x + 3 a function

Step by step

The question

Question: is y = −x + 3 a function?

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

One x in, one y out.

1 Draw the graph

Draw the grid.

Draw y = −x + 3.

It is a straight line.

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 = 1.

It hits the graph only once.

Any other vertical line also hits it only once.

3 Read the answer

No vertical line hits it two times.

So yes, it is a function.

4 Check

Let's check with numbers.

x = 1 gives y = 2.

Only one y.

The same answer!

Let's look back.

First: draw the graph.

Then: vertical line test.

Then: read the answer.

Last: check.