document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=403290>Question 403290</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose you have a function y = f(x) such that the domain of f(x) is 1 &#8804; x &#8804; 6 and the range of f(x) is &#8722;3 &#8804; y &#8804; 5.  What is the domain of f(2(x &#8722; 3)) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #285250 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=285250\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since the domain is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%3C=x%3C=6 ALIGN=MIDDLE  ALT=\"1%3C=x%3C=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, this means that the set of possible input values is {1,2,3,4,5,6}. Say for the sake of argument that we're only dealing with integers (to make things easy for us)\r<BR>\n" );
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document.write( "Now consider that instead of plugging in 'x', you plug in x-3. So this means that instead of plugging in x=1, you'll plug x-3=1-3=-2 into the function.\r<BR>\n" );
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document.write( "So this means that the domain of f(x-3) is now\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-3%3C=x-3%3C=6-3 ALIGN=MIDDLE  ALT=\"1-3%3C=x-3%3C=6-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "which becomes\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%3C=x-3%3C=3 ALIGN=MIDDLE  ALT=\"-2%3C=x-3%3C=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the domain of f(x-3) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2%3C=x-3%3C=3 ALIGN=MIDDLE  ALT=\"-2%3C=x-3%3C=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we're going to take it a step further. Instead of plugging in x-3, we're going to double it and plug in 2(x-3). So instead of plugging in -2, we're going to plug (-2)(2)=-4 into the function.\r<BR>\n" );
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document.write( "So this means that the domain becomes\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28-2%29%3C=2%28x-3%29%3C=2%283%29 ALIGN=MIDDLE  ALT=\"2%28-2%29%3C=2%28x-3%29%3C=2%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the domain of f(2(x-3)) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%3C=2%28x-3%29%3C=6 ALIGN=MIDDLE  ALT=\"-4%3C=2%28x-3%29%3C=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > given that the domain of f(x) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%3C=x%3C=6 ALIGN=MIDDLE  ALT=\"1%3C=x%3C=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Basically, the smallest number that the input 2(x-3) can be is -4 and the largest number that 2(x-3) can be is 6 </SPAN>\n" );
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