Question

Is this graph a function or not a function?

Answer 1

It is a function.

Explanation:

You can test if a graph is a function if you draw a vertical line anywhere on the graph and you see it hits two points.

This is the table for the graph.

`\left[\begin{array}{ccc}x&y\\-3&0\\0&1\\3&2\end{array}\right]`

Remember these rules:

• Each x value, or input, has its unique y value, or output
• If you draw a vertical line anywhere on the graph, it should only go through one point

We can check these two rules for this graph:

• Does each x value have its own, unique y value? Yes
• If you draw a vertical line anywhere on the graph, does it only go through one point? Yes, there are no overlaps

Keep in mind that two different x-values can have the same y value.

Figure 1:

It has two x values with the same y-values.

Figure 2 and 3:

The vertical line goes through two points. So the same x-value has two different y-values.

-Chetan K