document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=173795>Question 173795</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having trouble getting these two. Can someone please help me...please..Thank you..Evaluate the functions for the values of x given as 1, 2, 4, 8, and 16. Describe the differences in the rate at which each function changes with increasing values of x. \r<BR>\n" );
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document.write( "3.f(x) = 2x3 + 7x2 - x - 1 \r<BR>\n" );
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document.write( "5.f(x) = ln x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #129359 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=129359\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To evaluate a function, such as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2x%5E3%2B7x%5E2-x-1 ALIGN=MIDDLE  ALT=\"f%28x%29=2x%5E3%2B7x%5E2-x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, at a given value of the independent variable, substitute the value for every instance of the variable in the function and then do the appropriate arithmetic.\r<BR>\n" );
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document.write( "In general, if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2x%5E3%2B7x%5E2-x-1 ALIGN=MIDDLE  ALT=\"f%28x%29=2x%5E3%2B7x%5E2-x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28a%29=2a%5E3%2B7a%5E2-a-1 ALIGN=MIDDLE  ALT=\"f%28a%29=2a%5E3%2B7a%5E2-a-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Specifically: if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=2x%5E3%2B7x%5E2-x-1 ALIGN=MIDDLE  ALT=\"f%28x%29=2x%5E3%2B7x%5E2-x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=2%281%29%5E3%2B7%281%29%5E2-%281%29-1 ALIGN=MIDDLE  ALT=\"f%281%29=2%281%29%5E3%2B7%281%29%5E2-%281%29-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "All you need to do is the arithmetic, and then make the other substitutions/do the arithmetic for the other given values.\r<BR>\n" );
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document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=ln%28x%29 ALIGN=MIDDLE  ALT=\"f%28x%29=ln%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, just use your Windows built in calculator in Scientific mode.  Enter the number to be substituted for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and then click the 'ln' key.  Writing down two or three decimal places should be plenty.  For example, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%282%29=ln%282%29 ALIGN=MIDDLE  ALT=\"f%282%29=ln%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is approximately equal to 0.69314718055994530941723212145818 according to the Windows calculator, but an answer of 0.69 or 0.693 is probably good enough unless your instructor told to you respond with greater precision for some reason.\r<BR>\n" );
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document.write( "As to the rate of change of the function as the independent variable increases, your first function changes very fast except in the area of the local minimum and local maximum near the zeros of the function.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28x%29 ALIGN=MIDDLE  ALT=\"ln%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > always gets larger as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > increases, but at a much slower rate.  See below for a graph of the two functions, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28x%29 ALIGN=MIDDLE  ALT=\"ln%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the green one:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C600%2C-10%2C10%2C-10%2C10%2C2x%5E3%2B7x%5E2-x-1%2Cln%28x%29%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C600%2C-10%2C10%2C-10%2C10%2C2x%5E3%2B7x%5E2-x-1%2Cln%28x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
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