document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1159375>Question 1159375</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the range of the function g:x -> x^2 with the domain {-3,-2,-1,0,1,2}.<BR>\n" );
document.write( "Illustrate g by means of a graph. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #782388 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=782388\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "The notation g:x -> x^2 is another way of writing g(x) = x^2. The input is x and the rule is to square the input to get the output.\r<BR>\n" );
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document.write( "Because g(x) is the output, and so is y, we can say y = g(x)<BR>\n" );
document.write( "Therefore, y = x^2 is the same as g(x) = x^2\r<BR>\n" );
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document.write( "The domain is the set of allowed input values.\r<BR>\n" );
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document.write( "If we plug in x = -3, then we get<BR>\n" );
document.write( "y = x^2<BR>\n" );
document.write( "y = (-3)^2<BR>\n" );
document.write( "y = 9<BR>\n" );
document.write( "The input x = -3 leads to the output y = 9\r<BR>\n" );
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document.write( "The input x = -2 leads to the output y = 4 since...<BR>\n" );
document.write( "y = x^2<BR>\n" );
document.write( "y = (-2)^2<BR>\n" );
document.write( "y = (-2)*(-2)<BR>\n" );
document.write( "y = 4\r<BR>\n" );
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document.write( "And so on. You do this for every value in the domain to get this table of values<BR>\n" );
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document.write( "<tr><TD >x</TD><TD >y</TD></tr><tr><TD >-3</TD><TD >9</TD></tr><tr><TD >-2</TD><TD >4</TD></tr><tr><TD >-1</TD><TD >1</TD></tr><tr><TD >0</TD><TD >0</TD></tr><tr><TD >1</TD><TD >1</TD></tr><tr><TD >2</TD><TD >4</TD></tr><tr><TD >3</TD><TD >9</TD></tr>\n" );
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document.write( "The range is the set of possible y outputs, given the specific domain. In this case, the range is {0, 1, 4, 9}. \r<BR>\n" );
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document.write( "We see that there's some symmetry going on as this graph shows below<BR>\n" );
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document.write( "I have not connected the points with a parabolic curve because the domain is very specific: we can only allow the values -3, -2, -1, 0, 1, 2\r<BR>\n" );
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document.write( "In other words, something like x = 1.5 is not allowed in the domain which is why the portion between x = 1 and x = 2 is not connected with a piece of a curve. The same applies to any other x value not in the domain. This is why we leave the graph as a series of discrete points.<BR>\n" );
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