document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1116577>Question 1116577</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine whether the graph of y = |x| &#8722; 3 is symmetric with respect to the origin, the x-axis, or the y-axis.<BR>\n" );
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document.write( "a. symmetric with respect to the x-axis only<BR>\n" );
document.write( "b.symmetric with respect to the y-axis only<BR>\n" );
document.write( "c. symmetric with respect to the origin only<BR>\n" );
document.write( "d. not symmetric with respect to the x-axis, not symmetric with respect to the y-axis, and<BR>\n" );
document.write( "not symmetric with respect to the origin </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #731502 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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/cgi-bin/show-face.mpl?user=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=731502\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Symmetry checks:\r<BR>\n" );
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document.write( "f(x) = f(-x)  ==>  symmetric with respect to y-axis<BR>\n" );
document.write( "f(x) = -f(x)  ==>  symmetric with respect to x-axis<BR>\n" );
document.write( "f(x) = -f(-x) ==> symmetric with respect to origin<br>\r<BR>\n" );
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document.write( "Which of these hold for  y = |x| - 3?   <br>\r<BR>\n" );
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document.write( "If you replace x with -x,  will f(x) change?   Try a value, say x=7.  f(7) = |7|-3 = 4.   f(-7) = |-7|-3 = 4.  <BR>\n" );
document.write( "No, f(x) does not change because of the absolute value operation.  So f(x) <em>is</em> symmetric with respect to the y-axis. <br>\r<BR>\n" );
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document.write( "Clearly f(x) does not equal -f(x), so no symmetry with respect to the x-axis.   (Note that a true \"function\" can not be symmetrical with respect to the x-axis because it would violate the vertical line test, i.e. it would not be one-to-one). <br> \r<BR>\n" );
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document.write( "f(x) clearly does not equal -f(-x) here either, so no symmetry with respect to the origin. <br>\r<BR>\n" );
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document.write( "Ans: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%28+b+%29+ ALIGN=MIDDLE  ALT=\"+highlight%28+b+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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