**How to determine a function from a graph :**

An effective tool that determines a function from a graph is "Vertical line test"

The following are the steps of vertical line test :

**Step 1 : **

Draw a vertical line at any where on the given graph.

**Step 2 : **

We have to check whether the vertical line drawn on the graph intersects the graph in at most one point.

**Step 3 : **

If the vertical line intersects the graph in at most one point, then the given graph represents a function.

If the vertical line intersects the graph in more than one point, then the given graph does not represent a function.

**Caution : **

For some graphs, the vertical line will intersect the graph in one point at one position and more than one point at a different position.

In the above situation, the graph will not represent a function.

**Key concept :**

A graph represents a function only if every vertical line intersects the graph in at most one point.

We can have better understanding on vertical line test for functions through the following examples.

**Example 1 : **

Use the vertical line test to determine whether the following graph represents a function.

**Solution : **

**Step 1 : **

Draw a vertical line at any where on the given graph.

**Step 2 : **

We have to check whether the vertical line drawn on the graph intersects the graph in at most one point.

**Step 3 : **

In the above graph, the vertical line intersects the graph in at most one point, then the given graph represents a function.

**Example 2 : **

Use the vertical line test to determine whether the following graph represents a function.

**Solution : **

**Step 1 : **

Draw a vertical line at any where on the given graph.

**Step 2 : **

We have to check whether the vertical line drawn on the graph intersects the graph in at most one point.

**Step 3 : **

In the above graph, the vertical line intersects the graph in more than one point (three points), then the given graph does not represent a function.

After having gone through the stuff given above, we hope that the students would have understood "How to determine a function from a graph".

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