document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=859694>Question 859694</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi there again! Keeping with my schedule with pre-calculus learning, now i'm struggling with a problem on absolute value function. Said function is this one:\r<BR>\n" );
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document.write( " f(x) = ||3x + 2| - 3|\r<BR>\n" );
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document.write( "Its an absolute value inside another absolute value!!! I stopped when i got this  absolut value of a piecewise function:\r<BR>\n" );
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document.write( "         g(x) = <BR>\n" );
document.write( "  | 3x - 1 if x >= 1/3 |<BR>\n" );
document.write( "  | -3x + 5 if x < 1/3 |\r<BR>\n" );
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document.write( "So, any help or hint on how to work this out i would be glad!!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #517911 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=517911\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is not a full solution, but it should at least help you to understand the given function better.\r<BR>\n" );
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document.write( "The function will be positive, regardless of the x value used.\r<BR>\n" );
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document.write( "Deep inside, 3x+2=0 when?<BR>\n" );
document.write( "3x+2=0 at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-%282%2F3%29 ALIGN=MIDDLE  ALT=\"x=-%282%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, may be a critical point.\r<BR>\n" );
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document.write( "Out from that by one level, when does <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=abs%283x%2B2%29=3 ALIGN=MIDDLE  ALT=\"abs%283x%2B2%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ?<BR>\n" );
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document.write( "If x<0 then -3x-2=3,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-5%2F3 ALIGN=MIDDLE  ALT=\"x=-5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, a critical point.<BR>\n" );
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document.write( "If x>=0 then 3x+2=3,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1%2F3 ALIGN=MIDDLE  ALT=\"x=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, a critical point.<BR>\n" );
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document.write( "The three different critical points cut the x axis into four intervals, and you can find what the function definition would be in each interval, without expressing the function definition parts in absolute value.  \r<BR>\n" );
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document.write( "Summary of the intervals based on these critical points:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2F3%3C=x%3C-2%2F3 ALIGN=MIDDLE  ALT=\"-5%2F3%3C=x%3C-2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%2F3%3C=x%3C1%2F3 ALIGN=MIDDLE  ALT=\"-2%2F3%3C=x%3C1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3%3C=x%3Coo ALIGN=MIDDLE  ALT=\"1%2F3%3C=x%3Coo\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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