document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=81712>Question 81712</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given f(x) = –2x – 1, find f(a – 3). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #58569 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=58569\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given f(x)=-2x-1, find f(a-3)<BR>\n" );
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document.write( "f(a-3) tells you to replace x with the quantity (a-3). When you do that replacement,<BR>\n" );
document.write( "the original equation for f(x) becomes:<BR>\n" );
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document.write( "f(a-3) = -2(a-3) - 1<BR>\n" );
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document.write( "Do the distributed multiplication on the right side by multiplying -2 times each of the two<BR>\n" );
document.write( "terms in the parentheses to get:<BR>\n" );
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document.write( "f(a-3) = -2a + 6 - 1<BR>\n" );
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document.write( "Simplify by combining the +6 and -1 to get:<BR>\n" );
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document.write( "f(a-3) = -2a + 5<BR>\n" );
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document.write( "To graph this equation, replace f(a-3) by y and you have:<BR>\n" );
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document.write( "y = -2a + 5<BR>\n" );
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document.write( "Call the vertical axis the y-axis and the horizontal axis the a-axis.<BR>\n" );
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document.write( "The equation y = -2a + 5 is in the slope intercept form.  If you set \"a\" equal to zero, the <BR>\n" );
document.write( "equation reduces to y = +5.  This tells you that the point (0, 5) is on the graph.<BR>\n" );
document.write( "But this point identifies the value where the graph intersects the y-axis. <BR>\n" );
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document.write( "You can also set y equal to zero, and when you do that the equation becomes:<BR>\n" );
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document.write( "0 = -2a + 5<BR>\n" );
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document.write( "Add +2a to both sides to eliminate the -2a on the right side, and the equation changes to:<BR>\n" );
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document.write( "2a = +5<BR>\n" );
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document.write( "Divide both sides by the multiplier of the a on the left side to get:<BR>\n" );
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document.write( "a = 5/2 = 2.5<BR>\n" );
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document.write( "This tells you that when y = 0 then a =  2.5 so the point (2.5, 0) is on the graph, and this<BR>\n" );
document.write( "point is on the a-axis at 2.5.<BR>\n" );
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document.write( "You now have two points on the graph. If you plot these two points, you can then use a <BR>\n" );
document.write( "straight edge to extend a line through them.  Note that from the slope intercept form of<BR>\n" );
document.write( "the equation [y = -2a + 5] the slope is the multiplier of the \"a\" term. In this case that<BR>\n" );
document.write( "multiplier is -2. So the graph you have created has a slope of -2 and you can check<BR>\n" );
document.write( "your graphed line to make sure that for any point on the line, if you move horizontally<BR>\n" );
document.write( "1 unit from that point and then move 2 units down you should be back on the graphed line.<BR>\n" );
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document.write( "When you get done, you should have a graph that looks like this except the label on the<BR>\n" );
document.write( "horizontal axis should be \"a\" instead of \"x\":<BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better.<BR>\n" );
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