document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=78018>Question 78018</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Graph the function and state the domain and range.\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=abs%28x-2%29 ALIGN=MIDDLE  ALT=\"y=abs%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #55944 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=55944\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=abs%28x-2%29 ALIGN=MIDDLE  ALT=\"y=abs%28x-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "The easiest way to graph this is to plot some values.  If you think about it, one value to<BR>\n" );
document.write( "look at is when x = +2.  Why? Because when x = 2 the term inside the absolute value signs<BR>\n" );
document.write( "becomes +2 - 2 or zero, and therefore, y = 0.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Next, you can find out what the value of y is when the graph crosses the y-axis. You can do<BR>\n" );
document.write( "that by letting x = 0. (Think about it ... by setting x = 0, the corresponding value of<BR>\n" );
document.write( "y has to be on the y-axis.)  When x = 0 the quantity inside the absolute value signs becomes<BR>\n" );
document.write( "0 - 2 = -2. And when you take the absolute value of -2 you get +2.  So when x = 0 the corresponding<BR>\n" );
document.write( "value of y is +2.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Next try a few negative values of x. Let's let x = -5 and you get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+abs%28-5+-+2%29+=+abs%28-7%29+=+%2B7 ALIGN=MIDDLE  ALT=\"y+=+abs%28-5+-+2%29+=+abs%28-7%29+=+%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now let x = -8 and you get:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+abs%28-8+-+2%29+=+abs%28-10%29+=+%2B10 ALIGN=MIDDLE  ALT=\"y+=+abs%28-8+-+2%29+=+abs%28-10%29+=+%2B10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Next let's look at a few positive values of x.  Let's give x a value of +5.  The equation<BR>\n" );
document.write( "becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+abs%285+-+2%29+=+abs%283%29+=+%2B3 ALIGN=MIDDLE  ALT=\"y+=+abs%285+-+2%29+=+abs%283%29+=+%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Now let's give x a value of +8. The equation then becomes:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+abs%288+-+2%29+=+abs%286%29+=+%2B6 ALIGN=MIDDLE  ALT=\"y+=+abs%288+-+2%29+=+abs%286%29+=+%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "In summary, we know that the following are points on the graph:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(+2, 0); (0, +2); (-5, +7); (-8, + 10); (+5, +3), (+8, +6)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "You can get more points if you like by doing the same sort of process with different<BR>\n" );
document.write( "values of x.  Let's draw the graph and then discuss the domain and range.  The graph is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C+-15%2C%2B15%2C-5%2C%2B20%2Cabs%28x-2%29%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C+-15%2C%2B15%2C-5%2C%2B20%2Cabs%28x-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "By looking at the graph, you can see that there is no limit on the value of x.  You can<BR>\n" );
document.write( "assign to x any value from minus infinity to plus infinity.  However, look at the values<BR>\n" );
document.write( "that y can take (the range).  You can get y = 0 and y = any positive value, depending<BR>\n" );
document.write( "on what value you assign to x. But you can never get a value of y that is negative.<BR>\n" );
document.write( "So you can say that y must be equal to or greater than zero. In summary the domain is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "-oo < x < + oo (where oo stands for infinity)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "and the range is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "0 <= y (where <= represents greater than or equal to)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Hope this helps you to understand the concept of absolute value a little more. When you<BR>\n" );
document.write( "take the absolute value of a quantity, the result is a positive value. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );