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### 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}

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

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Basic Algebra
High School Functions

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