document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205034>Question 1205034</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph the function for two periods.<BR>\n" );
document.write( "f(x)=tan(x)-2<BR>\n" );
document.write( "Identify the stretching factor and midline equation.<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 #841638 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=841638\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Graph the function for two periods.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=tan%28x%29-2 ALIGN=MIDDLE  ALT=\"f%28x%29=tan%28x%29-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-7%2C+7%2C+-7%2C+7%2C++tan%28x%29-2%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-7%2C+7%2C+-7%2C+7%2C++tan%28x%29-2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Identify the stretching factor and midline equation.\r<BR>\n" );
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document.write( "Tangent Function of the Form \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+a+%2Atan+%28b%28x+-+h%29%29+%2B+k ALIGN=MIDDLE  ALT=\"y+=+a+%2Atan+%28b%28x+-+h%29%29+%2B+k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >  -  gives the amplitude, or vertical stretch or compression, for the function.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >  -  indicates the horizontal compression factor for the function. <BR>\n" );
document.write( " the period= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F+b ALIGN=MIDDLE  ALT=\"pi%2F+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+ ALIGN=MIDDLE  ALT=\"h+\"   DISABLED_style= \"max-width:90%; height:auto;\" >-gives the horizontal shift for the function.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   DISABLED_style= \"max-width:90%; height:auto;\" > - gives the vertical shift for the function.\r<BR>\n" );
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document.write( "The graph of tangent has no maximum or minimum value. Therefore, tangent is an example of a periodic function with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=NO+ ALIGN=MIDDLE  ALT=\"NO+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=midline ALIGN=MIDDLE  ALT=\"midline\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+amplitude ALIGN=MIDDLE  ALT=\"+amplitude\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=tan%28x%29-2+ ALIGN=MIDDLE  ALT=\"f%28x%29=tan%28x%29-2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "In this case, <BR>\n" );
document.write( " amplitude: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=none ALIGN=MIDDLE  ALT=\"none\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=1 ALIGN=MIDDLE  ALT=\"b=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the period of tangent is<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+pi%2Fb=pi%2F1=pi ALIGN=MIDDLE  ALT=\"+pi%2Fb=pi%2F1=pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=0 ALIGN=MIDDLE  ALT=\"h+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >-indicates there is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=no ALIGN=MIDDLE  ALT=\"no\"   DISABLED_style= \"max-width:90%; height:auto;\" > horizontal shift <BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k+=+-2 ALIGN=MIDDLE  ALT=\"k+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, indicating a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=vertical+ ALIGN=MIDDLE  ALT=\"vertical+\"   DISABLED_style= \"max-width:90%; height:auto;\" >shift of two units <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=down ALIGN=MIDDLE  ALT=\"down\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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