document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=162729>Question 162729</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The functions are f(x)=2x^2+5x+7 and g(x)=x^3 + 2<BR>\n" );
document.write( "The directions say evaluate the following: and identify the domain of each <BR>\n" );
document.write( "(f+g)(x)<BR>\n" );
document.write( "I got x^3+2x^2+5x+9 but I dont know what the domain is.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #119965 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=119965\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your request:<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "The functions are f(x)=2x^2+5x+7 and g(x)=x^3 + 2<BR>\n" );
document.write( "The directions say evaluate the following: and identify the domain of each <BR>\n" );
document.write( "(f+g)(x)<BR>\n" );
document.write( "I got x^3+2x^2+5x+9 but I dont know what the domain is.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "my answer:<BR>\n" );
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document.write( "f+g(x) = f(x) + g(x)<BR>\n" );
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document.write( "you got it right again.<BR>\n" );
document.write( "domain is all x since nothing to make the answer imaginary or cause a division by 0.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "in general, if the domain is not specified, then the domain is whatever makes the range valid.<BR>\n" );
document.write( "there will be 4 graphs.<BR>\n" );
document.write( "scan down after each one to get the next plus any additional comments.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "graph of f+g(x) is graph of x^3+2x^2+5x+9 shown below<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28800%2C800%2C-9%2C9%2C-1000%2C1000%2Cx%5E3%2B2%2Ax%5E2%2B5%2Ax%2B9%29 ALIGN=MIDDLE  ALT=\"graph%28800%2C800%2C-9%2C9%2C-1000%2C1000%2Cx%5E3%2B2%2Ax%5E2%2B5%2Ax%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "graph of g-f(x) is graph of x^3-2x^2-5x-5 shown below<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28800%2C800%2C-9%2C9%2C-600%2C600%2Cx%5E3-2%2Ax%5E2-5%2Ax-5%29 ALIGN=MIDDLE  ALT=\"graph%28800%2C800%2C-9%2C9%2C-600%2C600%2Cx%5E3-2%2Ax%5E2-5%2Ax-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "graph of f*g(x) is graph of x^5 + 5x^4 + 7x^3 + 4x^2 + 10x + 14 shown below<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28800%2C800%2C-9%2C9%2C-50000%2C100000%2Cx%5E5%2B5%2Ax%5E4%2B7%2Ax%5E3%2B4%2Ax%5E2%2B10%2Ax%2B14%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "graph of f/g(x) is graph of (2x^2+5x+7)/(x^3+2) shown below<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28800%2C800%2C-9%2C9%2C-10%2C10%2C%282%2Ax%5E2%2B5%2Ax%2B7%29%2F%28x%5E3%2B2%29%29 ALIGN=MIDDLE  ALT=\"graph%28800%2C800%2C-9%2C9%2C-10%2C10%2C%282%2Ax%5E2%2B5%2Ax%2B7%29%2F%28x%5E3%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "it appears that the graph is good for all values of x except at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2%29%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"x+=+%28-2%29%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where the value is undefined.<BR>\n" );
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document.write( "as x^3 approaches -2 from the right (x^3 is greater than -2), the graph goes positive in a big way.<BR>\n" );
document.write( "for example:<BR>\n" );
document.write( "if you make x^3 = (-1.9999999999999), which is greater than -2, you'll see that the value of y becomes 3.86114E+13 which is a very large positive number. <BR>\n" );
document.write( "----- <BR>\n" );
document.write( "as x^3 approaches -2 from the left (x^3 is smaller than -2), the graph goes negative in a big way.<BR>\n" );
document.write( "for example:<BR>\n" );
document.write( "if you make x^3 = (-2.0000000000001). which is less than -2, you'll see that the value of y becomes -3.89561E+13 which is a very large negative number.<BR>\n" );
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document.write( "the graph does not appear to be able to show this as the intervals between x values appear to be too small to be captured.\r<BR>\n" );
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