document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=64826>Question 64826</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If f(x) = 2x, describe the transformation of the curve for g(x) = -2 x-2\r<BR>\n" );
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document.write( "I desparetely need help with this thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #45686 by </B><A HREF=/tutors/aboutme.mpl?userid=mszlmb><B>mszlmb(115)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mszlmb><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=mszlmb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=45686\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <blockquote>\"If f(x) = 2x, describe the transformation of the curve for g(x) = -2 x-2\r<BR>\n" );
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document.write( "I desparetely need help with this thank you\"</blockquote>\r<BR>\n" );
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document.write( "I assume you mean the <b>line</b> rather than the 'curve,' as both f(x) and g(x) are linear.  For the record, here is a graph of both:<br>\r<BR>\n" );
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document.write( "<center><b>F(x)=2x</b><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28200%2C200%2C-10%2C10%2C-10%2C10%2C2x%29 ALIGN=MIDDLE  ALT=\"graph%28200%2C200%2C-10%2C10%2C-10%2C10%2C2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<b>G(x)=-2x-2</b><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28200%2C200%2C-10%2C10%2C-10%2C10%2C-2x-2%29 ALIGN=MIDDLE  ALT=\"graph%28200%2C200%2C-10%2C10%2C-10%2C10%2C-2x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></center><br>\r<BR>\n" );
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document.write( "What the question is basically asking is 'How does G differ from F?'<br>\r<BR>\n" );
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document.write( "To get from F to G, first we make the \"2x\" <i>negative</i>.  What happens when you make something negative?  They are 'flipped' along the horizontal axis.  Here are some examples:<BR>\n" );
document.write( "<center><b>Graph of F(x)=x</b><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28200%2C200%2C-10%2C10%2C-10%2C10%2Cx%29 ALIGN=MIDDLE  ALT=\"graph%28200%2C200%2C-10%2C10%2C-10%2C10%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<b>Graph of F(x)=-x</b><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28200%2C200%2C-10%2C10%2C-10%2C10%2C-x%29 ALIGN=MIDDLE  ALT=\"graph%28200%2C200%2C-10%2C10%2C-10%2C10%2C-x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></center><BR>\n" );
document.write( "See how they're flipped along the horizontal (x) axis?  Let's look at another:<BR>\n" );
document.write( "<center><b>Graph of F(x)=x/2</b><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28200%2C200%2C-10%2C10%2C-10%2C10%2Cx%2F2%29 ALIGN=MIDDLE  ALT=\"graph%28200%2C200%2C-10%2C10%2C-10%2C10%2Cx%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<b>Graph of F(x)=-x/2</b><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28200%2C200%2C-10%2C10%2C-10%2C10%2C-x%2F2%29 ALIGN=MIDDLE  ALT=\"graph%28200%2C200%2C-10%2C10%2C-10%2C10%2C-x%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></center><br>\r<BR>\n" );
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document.write( "So, the graph of -2x in regard to 2x, is flipped;<BR>\n" );
document.write( "<center><b>Graph of F(x)=2x</b><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28200%2C200%2C-10%2C10%2C-10%2C10%2C2x%29 ALIGN=MIDDLE  ALT=\"graph%28200%2C200%2C-10%2C10%2C-10%2C10%2C2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<b>Graph of F(x)=-2x</b><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28200%2C200%2C-10%2C10%2C-10%2C10%2C-2x%29 ALIGN=MIDDLE  ALT=\"graph%28200%2C200%2C-10%2C10%2C-10%2C10%2C-2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></center><br>\r<BR>\n" );
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document.write( "But then we <b>subtract two</b>, what does <I>that</i> do to the graph??  Here are some examples to help verify.  Adding or subtracting to a linear equation (an equation in the form of y=mx+b) moves it along the vertical (y) axis:<BR>\n" );
document.write( "<center><b>Graph of F(x)=x</b><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28200%2C200%2C-10%2C10%2C-10%2C10%2Cx%29 ALIGN=MIDDLE  ALT=\"graph%28200%2C200%2C-10%2C10%2C-10%2C10%2Cx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<b>Graph of F(x)=x+2</b><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28200%2C200%2C-10%2C10%2C-10%2C10%2Cx%2B2%29 ALIGN=MIDDLE  ALT=\"graph%28200%2C200%2C-10%2C10%2C-10%2C10%2Cx%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "You know, let's have some fun with this.  Following is a graph of the function Y=X+1, y=x+2, y=x+3, etc., and y=x+0, y=x-1, y=x-2, etc.  Just to illustrate the point; these are all on the same graph:  <font color=red>[EDIT: Upon reviewing, I found that many of the lines are white.  They're plotted, but they're white.  They'll look like cutouts of the x and y axes.]</font>  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28200%2C200%2C-10%2C10%2C-10%2C10%2CX-10%2Cx-9%2Cx-8%2Cx-7%2Cx-6%2Cx-5%2Cx-4%2Cx-3%2Cx-2%2Cx-1%2Cx%2Cx%0D%0A%2B1%2Cx%2B2%2Cx%2B3%2Cx%2B4%2Cx%2B5%2Cx%2B6%2Cx%2B7%2Cx%2B8%2Cx%2B9%2Cx%2B10%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Pretty cool, huh?  You see, adding any amount to x moves it up that amount, and subtracting an amount <i>from</i> x moves it down that amount.  Therefore, <strong>the difference between f(x)=2x and g(x)=2x-2 is that G(x) moves down two.</strong>  Notice I didn't include g(x)=<b>-</b>2x-2.\r<BR>\n" );
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document.write( "Well, making it negative flips it along the x axis (horizontally), and subtracting 2 from it moves it down two units.  Thus, the transformation is <b>the line is flipped along the x axis and moved two units down.</b><BR>\n" );
document.write( "Here are the anticipated graphs:<BR>\n" );
document.write( "<center><b>F(x)=2x</b><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C2x%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<b>G(x)=-2x-2</b><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C-2x-2%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C-2x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></center><br>\r<BR>\n" );
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document.write( "You'll notice that G(x) is simply F(x)'s function flipped along the x axis and moved down 2.  It's as simple as that!  Any questions, feel free to ask. </SPAN>\n" );
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