document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=81747>Question 81747</A>: <I><SPAN STYLE=\"word-break: break-all;\"> would someone help me to figure out how to find the second part of this problem and graph it please. Thanks\r<BR>\n" );
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document.write( "Given f(x)=-x-4, 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 #58563 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=58563\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given f(x)=-x-4, 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) = -(a-3) - 4<BR>\n" );
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document.write( "When you remove the parentheses on the right side, the minus sign in front of the parentheses<BR>\n" );
document.write( "require you to change the signs of all the terms in the parentheses.  Applying this rule<BR>\n" );
document.write( "changes the equation to:<BR>\n" );
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document.write( "f(a-3) = -a + 3 -4<BR>\n" );
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document.write( "Finally, simplify by combining the +3 and -4 to get:<BR>\n" );
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document.write( "f(a-3) = -a - 1<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 = -a - 1<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 = -a - 1 is in the slope intercept form.  If you set a equal to zero, the <BR>\n" );
document.write( "equation reduces to y = -1.  This tells you that the point (0, -1) 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 = -a - 1<BR>\n" );
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document.write( "Add +a to both sides to eliminate the -a on the right side, and the equation changes to:<BR>\n" );
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document.write( "a = -1<BR>\n" );
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document.write( "This tells you that when y = 0 then a = -1 so the point (-1, 0) is on the graph, and this<BR>\n" );
document.write( "point is on the a-axis at -1.<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 = -a -1] the slope is the multiplier of the \"a\" term. In this case that<BR>\n" );
document.write( "multiplier is -1. So the graph you have created has a slope of -1 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 1 unit 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( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph+%28300%2C300%2C-10%2C10%2C-10%2C10%2C-x+-1%29 ALIGN=MIDDLE  ALT=\"graph+%28300%2C300%2C-10%2C10%2C-10%2C10%2C-x+-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><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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