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/