**Identifying functions worksheet with answers :**

Here we are going to see some practice questions on identifying functions.

**Question 1 :**

**Use the vertical line test to determine which of the following graphs represent a function.**

**Question 2 :**

**Use the vertical line test to determine which of the following graphs represent a function.**

**Question 3 :**

**Use the vertical line test to determine which of the following graphs represent a function.**

**Question 4 :**

**Use the vertical line test to determine which of the following graphs represent a function.**

For many functions we can obtain its graph. But not every graph will represent a function. Following test helps us in determining if the given graph is a function or not.

**Vertical line test for functions :**

This is a tool which can be used to test whether the given graph represents a function or not.

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.

Let us see some examples to understand how to tell if the graph is a function or not.

**Problem 1 :**

Use the vertical line test to determine which of the following graphs represent a function.

**Solution :**

The given graph does not represent a function as a vertical line cuts the graph at two points P and Q.

**Example 2 :**

Use the vertical line test to determine which of the following graphs represent a function.

**Solution :**

The given graph represents a function as any vertical line will intersect the graph at most one point P.

**Example 3 :**

Use the vertical line test to determine which of the following graphs represent a function.

**Solution :**

The given graph does not represent a function as a vertical line cuts the graph at two points A and B.

**Example 4 :**

Use the vertical line test to determine which of the following graphs represent a function.

**Solution : **

The given graph represents a function as the graph satisfies the vertical line test.

After having gone through the stuff given above, we hope that the students would have understood "Identifying functions worksheet with answers".

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