document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=607288>Question 607288</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph the function f(x)= -x, X<3, <BR>\n" );
document.write( "                         3x-4, x>= 3<BR>\n" );
document.write( "a) fund the domain<BR>\n" );
document.write( "b) locate any intercepts<BR>\n" );
document.write( "c) graph the function<BR>\n" );
document.write( "d) find the range<BR>\n" );
document.write( "e) is f continuous on its domain? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #382626 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=382626\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) The function is defined in two different ways for x<3 and for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=3 ALIGN=MIDDLE  ALT=\"x%3E=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but it is defined for all x, so the domain is all the real numbers.<BR>\n" );
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document.write( "b) For x<3, f(x)=-x is a straight line going through the origin, since f(0)=0, so you could say that the x-intercept and the y-intercept are (0,0).<BR>\n" );
document.write( "In the other part of the function, for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=3 ALIGN=MIDDLE  ALT=\"x%3E=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%3E=9 ALIGN=MIDDLE  ALT=\"3x%3E=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=3x-4%3E=9-5=4%3E0 ALIGN=MIDDLE  ALT=\"f%28x%29=3x-4%3E=9-5=4%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > , so there are no intercepts (no x=0 and no y=0) in that part of the function.<BR>\n" );
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document.write( "c) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-5%2C5%2C-4%2C11%2C%0D%0Agrid%281%29%2C%0D%0Ablue%28line%283%2C4%2C6%2C13%29%29%2C%0D%0Ablue%28line%28-5%2C5%2C2.8%2C-2.8%29%29%2C%0D%0Ablue%28circle%283%2C-3%2C0.2%29%29%2Cblue%28circle%283%2C4%2C0.1%29%29%2C%0D%0Ablue%28circle%283%2C4%2C0.06%29%29%2Cblue%28circle%283%2C4%2C0.03%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "d) f(x)>-3 on both parts of the function, but there is no upper limit. Maybe you would describe the range as (-3,infinity), or maybe you are expected to use a different notation.<BR>\n" );
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document.write( "e) No. The function is obviously discontinuous at x=3. While it is continuous at all other points of its domain, it is not continuous at all points of the domain. </SPAN>\n" );
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