document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=82150>Question 82150</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If P(4,-5) is a point on the graph of the function y=f(x), find the corresponding point on the graph of y=2f(x-6).  The answer is multiple choice.\r<BR>\n" );
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document.write( "a. (1,8)<BR>\n" );
document.write( "b. (2,-5)<BR>\n" );
document.write( "c. (6,8)<BR>\n" );
document.write( "d. (10,-10) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #58848 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=58848\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If we're given y=2f(x-6), this tells us is to shift the original graph f(x)  6 units to the right and double every output. So we're essentially starting at x=4 (the x-coordinate of our point), shifting 6 units to the right (adding 6 to 4), and then doubling the output. So our new x-coordinate is x=10. We can easily verify this by sticking x=10 into f(x-6) to get:\r<BR>\n" );
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document.write( "f(10-6)=f(4)\r<BR>\n" );
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document.write( "which is our original point. To get our new y coordinate, we simply double the output (ie our old y-coordinate y=-5). So the corresponding point on y=2f(x-6) is \r<BR>\n" );
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document.write( "(10,-10) which is answer d)\r<BR>\n" );
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document.write( "If this is hard to grasp, make a function that goes through (4,-5) (for instance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28-5%2F4%29x ALIGN=MIDDLE  ALT=\"y=%28-5%2F4%29x\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and shift the function. So y=2f(x-6) would be \r<BR>\n" );
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document.write( "y=2f(x-6)-> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2%28-5%2F4%29%28x-6%29 ALIGN=MIDDLE  ALT=\"y=2%28-5%2F4%29%28x-6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and if we plug in x=10 (remember we've shifted 6 units to the right) we get y=-10, which verifies our answer.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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