document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=924258>Question 924258</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph each absolute value function and state its domain and range\r<BR>\n" );
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document.write( "y=|2x-3|\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "x+3=|y| </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #560741 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=560741\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This response is not a complete answer or solution but may be helpful.\r<BR>\n" );
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document.write( "The first equation will be only positive for any values of/ or all values of x.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=abs%282x-3%29 ALIGN=MIDDLE  ALT=\"y=abs%282x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > range is The Real Numbers greater than or equal to zero.  The Domain is all real numbers.  The critical x value at which sharp point corner occurs is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F2 ALIGN=MIDDLE  ALT=\"x=3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Your second given equation can be also expressed, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28y%5E2%29=x%2B3 ALIGN=MIDDLE  ALT=\"sqrt%28y%5E2%29=x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  This lets you find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2=%28x%2B3%29%5E2 ALIGN=MIDDLE  ALT=\"y%5E2=%28x%2B3%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Take square root of both sides gives you two branches:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-sqrt%28%28x%2B3%29%5E2%29 ALIGN=MIDDLE  ALT=\"y=-sqrt%28%28x%2B3%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sqrt%28%28x%2B3%29%5E2%29 ALIGN=MIDDLE  ALT=\"y=sqrt%28%28x%2B3%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "Finishing this,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=-%28x%2B3%29%29 ALIGN=MIDDLE  ALT=\"highlight%28y=-%28x%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  OR  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=x%2B3%29 ALIGN=MIDDLE  ALT=\"highlight%28y=x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "BUT look very carefully at the original equation again.<BR>\n" );
document.write( "The right member is never negative.  This means for DOMAIN, <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;\" >. </SPAN>\n" );
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