document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200349>Question 1200349</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Evaluate the piecewise defined function at the indicated values.\r<BR>\n" );
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document.write( "f(x) = {4x         if x<-4<BR>\n" );
document.write( "          { x+2      If -4<_ x <_ 5 <BR>\n" );
document.write( "          { (x-5)^2  if x > 5\r<BR>\n" );
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document.write( "f(-5)=<BR>\n" );
document.write( "f(-4)=<BR>\n" );
document.write( "f(4)=<BR>\n" );
document.write( "f(5)=<BR>\n" );
document.write( "f(8)= </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #834483 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=834483\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answers:<BR>\n" );
document.write( "f(-5)= <font color=red size=4>-20</font><BR>\n" );
document.write( "f(-4)= <font color=red size=4>-2</font><BR>\n" );
document.write( "f(4)= <font color=red size=4>6</font><BR>\n" );
document.write( "f(5)= <font color=red size=4>7</font><BR>\n" );
document.write( "f(8)= <font color=red size=4>9</font>\r<BR>\n" );
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document.write( "Explanation:\r<BR>\n" );
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document.write( "Piecewise functions are a Frankenstein of sorts because they have multiple functions glued together.\r<BR>\n" );
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document.write( "Another way to look at it is that the piecewise function has split identities.\r<BR>\n" );
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document.write( "The input x will determine which piece to use.<ul><li>If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3C+-4 ALIGN=MIDDLE  ALT=\"x+%3C+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+4x ALIGN=MIDDLE  ALT=\"f%28x%29+=+4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ></li><li>If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4+%3C=+x+%3C=+5 ALIGN=MIDDLE  ALT=\"-4+%3C=+x+%3C=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+x%2B2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ></li><li>If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E+5 ALIGN=MIDDLE  ALT=\"x+%3E+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%28x-5%29%5E2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%28x-5%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ></li></ul>If the input is x = -5, then we go for the interval <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3C+-4 ALIGN=MIDDLE  ALT=\"x+%3C+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Draw out a number line to see why this is the case.<BR>\n" );
document.write( "This means we pick the first piece.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+4x ALIGN=MIDDLE  ALT=\"f%28x%29+=+4x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-5%29+=+4%28-5%29 ALIGN=MIDDLE  ALT=\"f%28-5%29+=+4%28-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-5%29+=+-20 ALIGN=MIDDLE  ALT=\"f%28-5%29+=+-20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If the input is x = -4, then we go for the interval <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4+%3C=+x+%3C=+5 ALIGN=MIDDLE  ALT=\"-4+%3C=+x+%3C=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This time we go for the 2nd piece.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+x%2B2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-4%29+=+-4%2B2 ALIGN=MIDDLE  ALT=\"f%28-4%29+=+-4%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28-4%29+=+-2 ALIGN=MIDDLE  ALT=\"f%28-4%29+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We stick with the 2nd piece for the input x = 4, since it is also in the interval <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4+%3C=+x+%3C=+5 ALIGN=MIDDLE  ALT=\"-4+%3C=+x+%3C=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+x%2B2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%284%29+=+4%2B2 ALIGN=MIDDLE  ALT=\"f%284%29+=+4%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%284%29+=+6 ALIGN=MIDDLE  ALT=\"f%284%29+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Same goes for x = 5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+x%2B2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+x%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%285%29+=+5%2B2 ALIGN=MIDDLE  ALT=\"f%285%29+=+5%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%285%29+=+7 ALIGN=MIDDLE  ALT=\"f%285%29+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The last input x = 8 will involve the third piece, since we're now in the interval <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E+5 ALIGN=MIDDLE  ALT=\"x+%3E+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29+=+%28x-5%29%5E2 ALIGN=MIDDLE  ALT=\"f%28x%29+=+%28x-5%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%288%29+=+%288-5%29%5E2 ALIGN=MIDDLE  ALT=\"f%288%29+=+%288-5%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%288%29+=+%283%29%5E2 ALIGN=MIDDLE  ALT=\"f%288%29+=+%283%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%288%29+=+9 ALIGN=MIDDLE  ALT=\"f%288%29+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This is what the piecewise graph looks like<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-12%2C17%2C-34%2C38%2C%0D%0Agraph%28400%2C400%2C-12%2C17%2C-34%2C38%2C%0D%0A4x%2A%28%28sqrt%28-%28x%2B4.1%29%29%29%2F%28sqrt%28-%28x%2B4.1%29%29%29%29%2C%0D%0A%28x%2B2%29%2A%28%28sqrt%28-%28x%2B4%29%28x-5%29%29%29%2F%28sqrt%28-%28x%2B4%29%28x-5%29%29%29%29%2C%0D%0A%28x-5%29%5E2%2A%28%28sqrt%28x-5.3%29%29%2F%28sqrt%28x-5.3%29%29%29%29%2C%0D%0A%0D%0Ared%28circle%28-4%2C-16%2C0.5%29%29%2C%0D%0A%0D%0Agreen%28circle%28-4%2C-2%2C0.1%29%29%2C%0D%0Agreen%28circle%28-4%2C-2%2C0.2%29%29%2C%0D%0Agreen%28circle%28-4%2C-2%2C0.3%29%29%2C%0D%0Agreen%28circle%28-4%2C-2%2C0.4%29%29%2C%0D%0Agreen%28circle%28-4%2C-2%2C0.5%29%29%2C%0D%0A%0D%0A%0D%0Agreen%28circle%285%2C7%2C0.1%29%29%2C%0D%0Agreen%28circle%285%2C7%2C0.2%29%29%2C%0D%0Agreen%28circle%285%2C7%2C0.3%29%29%2C%0D%0Agreen%28circle%285%2C7%2C0.4%29%29%2C%0D%0Agreen%28circle%285%2C7%2C0.5%29%29%2C%0D%0A%0D%0Ablue%28circle%285%2C0%2C0.5%29%29%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The first piece 4x is in red. It is graphed only when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3C+-4 ALIGN=MIDDLE  ALT=\"x+%3C+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The second piece x+2 is in green. It is graphed only when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4+%3C=+x+%3C=+5 ALIGN=MIDDLE  ALT=\"-4+%3C=+x+%3C=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The third piece (x-5)^2 is in blue. It is graphed only when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%3E+5 ALIGN=MIDDLE  ALT=\"x+%3E+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "There are open holes at (-4, -16) and (5, 0)<BR>\n" );
document.write( "The open holes are not part of the graph. Think of them as potholes in the road.<BR>\n" );
document.write( "There are closed filled in endpoints at (-4, -2) and (5, 7)\r<BR>\n" );
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document.write( "I recommend either Desmos or GeoGebra as two graphing options.<BR>\n" );
document.write( "Here's the link to the interactive Desmos graph<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.desmos.com/calculator/jkfomczjuz\">https://www.desmos.com/calculator/jkfomczjuz</a><BR>\n" );
document.write( "This will allow you to zoom in/out, move the window around, etc.<BR>\n" );
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