Graphing Piecewise Functions

Date: 09/09/2001 at 23:19:36
From: Mary
Subject: Piecewise Functions (Algebra II)

I do not understand how to GRAPH piecewise functions. 

Graph:
          {2x  if 0<_ [that's less than or equal to] x<2}
     f(x)={4   if 2<x<4}
          {-1/4x +5 if 4<_ x<_6}

I know it is hard to understand what I wrote, but please help me!
Thank you so  much.
Mary

Date: 09/10/2001 at 08:51:30
From: Doctor Peterson
Subject: Re: Piecewise Functions (Algebra II)

Hi, Mary.

You have the function defined in three parts; you can start by marking 
the domains of those parts on the graph, by drawing (lightly) the 
vertical lines x = 0, x = 2, x = 4, and x = 6. Now, again lightly, 
draw the lines

    y = 2x

    y = 4

    y = -1/4 x + 5

Finally, you have to cut out the pieces that form the given function 
and glue them together (figuratively). Look in the region 0 <= x < 2, 
and darken the first line only within that region, that is, between 
the lines x = 0 and x = 2. Then, in the region 2 < x < 4, darken the 
second line, and in 4 <= x <= 6, darken the third line. The darkened 
portions consitute the function f(x), which is therefore defined only 
on the domain 0 <= x <= 6. 

In this case, you will find that the three segments actually are 
"glued" together; they meet at x = 2 and x = 4. That isn't always 
true, but when it is it can help you feel confident.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/