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### Recognizing Functions

```
Date: 09/30/2001 at 15:22:54
From: Miles
Subject: Recognizing functions

How do I know when there is a function on a graph?
```

```
Date: 09/30/2001 at 19:41:52
From: Doctor Jodi
Subject: Re: Recognizing functions

Hi Miles,

A function is something like this

IN
\   \
\   \____
|        |
|        |
|        |
----\   \
\   \
OUT

Where for each reasonable input, there's ONE output. Does this make
sense?

On a graph, we make the inputs x's and the output's y's. So the
condition means that for each x there's ONE y.

You can see if a graph is a function using the vertical line test.
Does any vertical line through the graph intersect more than one
place? If so, this ISN'T a function. But if EVERY vertical line
through the graph intersects in one place (or none), then this IS
a function.

Does that make sense?

Write back if you have more questions.

- Doctor Jodi, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Equations, Graphs, Translations
High School Functions

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