#### What is the Vertical Line Test for Functions?

**Answer: **A method to distinguish functions from relations

The vertical Line test

- is a way to determine if a relation is a function
- states that if a vertical line intersects the relation more than once, then the relation is a NOT a function.

If you think about it, the **vertical line test **is simply a restatement of the definition of a function

**Definition of a function: **Every x value has a unique y value.

*Think about it* If any particular x value has 2 different y values , then a vertical line will intersect the at two different places.

Let's examine the two relations below this These two relations differ by only 1 number!

**Practice** Problems

Ask yourself: "Can I draw a vertical line (anywhere) that will hit the graph two times ?"

**Answer: NO** vertical lines only hit the graph once so this ** is a function**

Ask yourself: "Can I draw a vertical line (anywhere) that will hit the graph two times ?"

**Answer: YES** a vertical line can hit the graph twice so this ** is not a function**

Ask yourself: "Can I draw a vertical line (anywhere) that will hit the graph two times ?"

**Answer: YES** a vertical line hits the graph several times , so this is ** not **is a function .

Ask yourself: "Can I draw a vertical line (anywhere) that will hit the graph two times ?"

**Answer: NO matter** where you try to draw a vertical line, it only hits the graph once so this **is a function**

Be careful at x =2. The point (2,1) is not filled in, indicating that the graph does not include the point (2,1). However, notice that (2,2) is completely filled in, because that point is included in the graph.

Ask yourself: "Can I draw a vertical line (anywhere) that will hit the graph two times ?"

**Answer: YES** vertical lines only hit the graph once so this ** is a function**

Unlike problem 3, in this case, the point (2,1) is filled in and is,therefore, included in the graph.

As you can see, that one point makes all the difference. this is not a function

Ask yourself: "Can I draw a vertical line (anywhere) that will hit the graph two times ?"

**Answer: YES** This is ** not a function **. In fact, circles, in general, are not functions

Ask yourself: "Can I draw a vertical line (anywhere) that will hit the graph two times ?"

**Answer: NO**This

**is a function**