{VERSION 4 0 "IBM INTEL NT" "4.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 
0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 258 "" 0 1 0 0 
0 0 0 1 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 
0 0 0 1 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
262 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 263 "" 0 1 0 0 
0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 1 0 0 0 0 0 
0 0 0 1 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 266 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
267 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 268 "" 0 1 0 0 
0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 269 "" 0 1 0 0 0 0 0 1 0 0 0 0 
0 0 0 1 }{CSTYLE "" -1 270 "" 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 1 }
{CSTYLE "" -1 271 "" 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 
272 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 273 "" 0 1 0 0 
0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 274 "" 0 1 0 0 0 0 1 0 0 0 0 0 
0 0 0 1 }{CSTYLE "" -1 275 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 276 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
277 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 278 "" 0 1 0 0 
0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 279 "" 0 1 0 0 0 0 1 0 0 0 0 0 
0 0 0 1 }{CSTYLE "" -1 280 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }
{CSTYLE "" -1 281 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 
282 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 283 "" 0 1 0 0 
0 0 1 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 284 "" 0 1 0 0 0 0 1 0 0 0 0 0 
0 0 0 1 }{CSTYLE "" -1 285 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }
{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" 
-1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 
-1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 258 1 {CSTYLE "
" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 
0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 69 "Lab 4 Maple Activities for
 Sept 12:  (Lesson 2 - Piecewise Functions)" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 258 9 "Ex
ample 1" }{TEXT -1 61 "  Let's use Maple to look at the following piec
ewise function" }{TEXT 257 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 256 "" 0 "" {TEXT -1 1 " " }{XPPEDIT 18 0 "f(x);" "6#-%\"fG6#%\"
xG" }{TEXT -1 4 " =  " }{XPPEDIT 18 0 "PIECEWISE([-2*x^2, x <= 1],[5-x
, 1 < x]);" "6#-%*PIECEWISEG6$7$,$*&\"\"#\"\"\"*$%\"xGF)F*!\"\"1F,F*7$
,&\"\"&F*F,F-2F*F," }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 37 "which we considered in lecture.  Then" }}
{PARA 0 "" 0 "" {TEXT -1 32 "(a)  find f(7), f(- 3), and f(1)" }}
{PARA 0 "" 0 "" {TEXT -1 27 "(b)  sketch the graph of  f" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 69 "The follo
wing line is how we would give Maple our piecewise function:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "f := x -> piecewise(x<=1, -2
*x^2, x>1, 5 - x);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 
"" 0 "" {TEXT -1 0 "" }{TEXT 256 7 "Notice:" }{TEXT -1 220 "  You ente
r the restriction for each piece of the piecewise function first.  The
n you enter the function for the restriction.  As always, it is a good
 idea to see if you have the function, which you want, by asking for  \+
" }{XPPEDIT 18 0 "f(x);" "6#-%\"fG6#%\"xG" }{TEXT -1 2 " ." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(x);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 46 "This is the piecewise fun
ction that we wanted." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 72 "Now, let's do Part (a) of this example an
d find f(7), f(- 3), and f(1): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 18 "f(7); f(-3); f(1);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 44 "Now, let's graph the function f using Map
le:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "plot(f(x),x, discont
=true, color=red);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 
"" 0 "" {TEXT -1 92 "Let's see if we can get a better graph by restric
ting the value of the y range on our graph:" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 48 "plot(f(x),x, y=-20..6, discont=true, color=red);" 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }{TEXT 259 7 "Notice:" }{TEXT -1 68 "  Our graph does not clearly sh
ow us the value of the function when " }{TEXT 260 1 "x" }{TEXT -1 35 "
 = 1, which is our \"breakup point.\"" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 261 0 "" }{TEXT 
262 9 "Example 2" }{TEXT 263 0 "" }{TEXT -1 43 "  Consider the followi
ng piecewise function" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 257 "" 
0 "" {TEXT -1 1 " " }{XPPEDIT 18 0 "g(x)" "6#-%\"gG6#%\"xG" }{TEXT -1 
3 " = " }{XPPEDIT 18 0 "PIECEWISE([sqrt(3-x), x < -1],[x^2-4, -1-x <= \+
0 and -3+x < 0],[2*x-1, 3 <= x]);" "6#-%*PIECEWISEG6%7$-%%sqrtG6#,&\"
\"$\"\"\"%\"xG!\"\"2F-,$F,F.7$,&*$F-\"\"#F,\"\"%F.31,&F,F.F-F.\"\"!2,&
F+F.F-F,F97$,&*&F4F,F-F,F,F,F.1F+F-" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 79 "Then (a)  find g(8), g(3), g(-1), and g(
- 6)  and  (b)  sketch the graph of  g." }}{PARA 258 "" 0 "" {TEXT -1 
3 "   " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 52 "To give Maple our piece
wise function, we would type:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 82 "g := x -> piecewise(x < -1, sqrt(3 - x), -1<=x and x <3, x^2 - 4
, x>= 3, 2*x - 1);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 
"" 0 "" {TEXT -1 87 "It is a good idea to check that we have the funct
ion, which we want, find asking for g(" }{TEXT 264 1 "x" }{TEXT -1 2 "
):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "g(x);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 
265 7 "Notice:" }{TEXT -1 42 "  In order to get the restriction  - 1 <
= " }{TEXT 266 1 "x" }{TEXT -1 81 " < 3, we have to type this compound
 inequality by its two parts, which are -1 <= " }{TEXT 267 1 "x" }
{TEXT -1 7 "  and  " }{TEXT 268 1 "x" }{TEXT -1 5 " < 3." }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 46 "(a)  Let'
s find g(8), g(3), g(-1), and g(- 6):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 26 "g(8); g(3); g(-1); g(- 6);" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 28 "(b)  To get the graph o
f  g:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "plot(g(x),x, disco
nt=true, color=red);" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 269 0 "" }{TEXT 270 9 "
Example 3" }{TEXT 271 0 "" }{TEXT -1 80 "  Let's have some Maple FUN! \+
 (But don't make a mess.)  Let's define a function " }{TEXT 272 1 "h" 
}{TEXT -1 64 " whose domain is the set of all real numbers and whose r
ange is " }{TEXT 273 23 "the graph of a function" }{TEXT -1 1 ":" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "h := c -> plot(piecewise(x<=
c, -2*x^2, x>c, 5 - x),x, y=-100..25, discont=true, color=red);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 67 "Un
fortunately, with this function, you will not be able to ask for " }
{TEXT 274 1 "h" }{TEXT -1 1 "(" }{TEXT 275 1 "c" }{TEXT -1 44 ") to ch
eck that you have the right function." }}{PARA 0 "" 0 "" {TEXT -1 11 "
Let's find " }{TEXT 276 1 "h" }{TEXT -1 4 "(1):" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 5 "h(1);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 277 7 "Notice:" }{TEXT -1 73 " \+
 This graph is the graph of our piecewise function from Example 1 abov
e." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 10 "Now
, find " }{TEXT 278 1 "h" }{TEXT -1 6 "(- 2):" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 6 "h(-2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 10 "Now, find " }{TEXT 279 1 "h" }{TEXT -1 
4 "(0):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "h(0);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 
280 5 "NOTE:" }{TEXT -1 46 "  You might need to change the restriction
 on " }{TEXT 281 1 "x" }{TEXT -1 8 " and/or " }{TEXT 282 1 "y" }{TEXT 
-1 35 " in the definition of the function " }{TEXT 283 1 "h" }{TEXT 
-1 41 " above in order to evaluate the function " }{TEXT 284 1 "h" }
{TEXT -1 37 " at some numbers.  For example, find " }{TEXT 285 1 "h" }
{TEXT -1 6 "(100)." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 
"" 0 "" {TEXT -1 102 "You can practice using Maple with piecewise func
tions using the piecewise functions from the textbook." }}}}{MARK "1 0
 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }