document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1001253>Question 1001253</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The function f is defined as follows.<BR>\n" );
document.write( "f(x)={x+6 if -5<=x<1}<BR>\n" );
document.write( "     {9 if x=1}<BR>\n" );
document.write( "     {-x+4 if x>1}\r<BR>\n" );
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document.write( "A.) Find the domain of the function<BR>\n" );
document.write( "B.)Locate any intercepts<BR>\n" );
document.write( "C.)Graph the function\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #618550 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=618550\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A)\r<BR>\n" );
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document.write( "The smallest x allowed is x = -5 (from the first piece of the piecewise function)<BR>\n" );
document.write( "There is no limit on the upper bound of x<BR>\n" );
document.write( "So the domain in interval notation is <font color=red>[-5, infinity)</font>\r<BR>\n" );
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document.write( "B)\r<BR>\n" );
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document.write( "Set each piece equal to 0 and solve for x\r<BR>\n" );
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document.write( "Piece 1:<BR>\n" );
document.write( "x+6 = 0<BR>\n" );
document.write( "x = -6<BR>\n" );
document.write( "But x = -6 is outside of the domain. So this is not a proper intercept\r<BR>\n" );
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document.write( "Piece 2:<BR>\n" );
document.write( "9 = 0 ... which is always false\r<BR>\n" );
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document.write( "Piece 3:<BR>\n" );
document.write( "-x+4 = 0<BR>\n" );
document.write( "-x = -4<BR>\n" );
document.write( "x = 4\r<BR>\n" );
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document.write( "So the only x intercept is the ordered pair/point <font color=red>(4,0)</font>\r<BR>\n" );
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document.write( "C)\r<BR>\n" );
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document.write( "To graph this piecewise function, you simply graph y = x+6, y = 9 and y = -x+4 but you apply the proper restrictions.\r<BR>\n" );
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document.write( "The graph of the piecewise function is shown below\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://i.imgur.com/FwSJaJQ.png\">\r<BR>\n" );
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document.write( "Notice how the red piece is the piece x+6 and it is only graphed from x = -5 to x = 1. There is a closed circle at x = -5 and an open circle at x = 1. The closed circle means \"include this point\" while the open circle means \"exclude this point\"\r<BR>\n" );
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document.write( "There is a single solitary point at (1,9). This represents the middle piece \"f(x) = 9 if x = 1\"\r<BR>\n" );
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document.write( "Finally, the last piece is -x+4 and is it the piece in green. It has an open circle at the endpoint and stretches on forever the more x increases. </SPAN>\n" );
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