document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=182277>Question 182277</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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. <BR>\n" );
document.write( "1.	f(x) = 2x – 5<BR>\n" );
document.write( "2.	f(x) = x2 - 4x + 3 <BR>\n" );
document.write( "3.	f(x) = x3 + 4x2 - 2x - 3<BR>\n" );
document.write( "4.	f(x) = 7x <BR>\n" );
document.write( "5.	f(x) = log x\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #136854 by </B><A HREF=/tutors/aboutme.mpl?userid=mastermath><B>mastermath(14)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mastermath><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=136854\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.	f(x) = 2x – 5\r<BR>\n" );
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document.write( "So, put x=1,2,4,8,16 and find the value of f(x)\r<BR>\n" );
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document.write( "f(1) = 2(1) - 5 = 2 - 5 = -3<BR>\n" );
document.write( "f(2) = 2(2) - 5 = 4 - 5 = -1<BR>\n" );
document.write( "f(4) = 2(4) - 5 = 8 - 5 = 3<BR>\n" );
document.write( "f(8) = 2(8) - 5 = 16 - 5 = 11<BR>\n" );
document.write( "f(16) = 2(16) - 5 = 32 - 5 = 27\r<BR>\n" );
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document.write( "So, as the value of x increases, f(x) also increases.<BR>\n" );
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document.write( "2.	f(x) = x2 - 4x + 3 \r<BR>\n" );
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document.write( "So, put x=1,2,4,8,16 and find the value of f(x)\r<BR>\n" );
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document.write( "f(1) = (1)^2 - 4(1) + 3 = 1 - 4 + 3 = 0<BR>\n" );
document.write( "f(2) = (2)^2 - 4(2) + 3 = 4 - 8 + 3 = -1<BR>\n" );
document.write( "f(4) = (4)^2 - 4(4) + 3 = 16 - 16 + 3 = 3<BR>\n" );
document.write( "f(8) = (8)^2 - 4(8) + 3 = 64 - 32 + 3 = 35<BR>\n" );
document.write( "f(16) = (16)^2 - 4(16) + 3 = 256 - 64 + 3 = 195\r<BR>\n" );
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document.write( "So,initially as the value of x increases, f(x) initially decreases from f(1) to f(2), but after that, as x increases, f(x) increases drastically.<BR>\n" );
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document.write( "3.      f(x) = x3 + 4x2 - 2x - 3\r<BR>\n" );
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document.write( "So, put x=1,2,4,8,16 and find the value of f(x)\r<BR>\n" );
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document.write( "f(1) = (1)^3 - 4(1)^2 -2(1) - 3 = 1 - 4(1) -2 - 3 = 1 - 4 - 5 = -8<BR>\n" );
document.write( "f(2) = (2)^3 - 4(2)^2 -2(2) - 3 = 8 - 4(4) -4 - 3 = 8 - 16 - 7 = -15<BR>\n" );
document.write( "f(4) = (4)^3 - 4(4)^2 -2(4) - 3 = 64 - 4(16) -8 - 3 = 64 - 64 - 11= -11<BR>\n" );
document.write( "f(8) = (8)^3 - 4(8)^2 -2(8) - 3 = 512 - 4(64) -16 - 3 = 512 - 256 - 19 = 237<BR>\n" );
document.write( "f(16) = (16)^3 - 4(16)^2 -2(16) - 3 = 4096 - 4(256) -32 - 3 = 4096 - 1024 - 35 = 3037\r<BR>\n" );
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document.write( "So,initially as the value of x increases, f(x) initially decreases from f(1) to f(2), but after that, as x increases, f(x) increases drastically.<BR>\n" );
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document.write( "4.	f(x) = 7x <BR>\n" );
document.write( "So, put x=1,2,4,8,16 and find the value of f(x)\r<BR>\n" );
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document.write( "f(1) = 7(1) = 7<BR>\n" );
document.write( "f(2) = 7(2) = 14<BR>\n" );
document.write( "f(4) = 7(4) = 28<BR>\n" );
document.write( "f(8) = 7(8) = 56<BR>\n" );
document.write( "f(16) = 7(16) = 112\r<BR>\n" );
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document.write( "So, as the value of x increases, f(x) also increases.<BR>\n" );
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document.write( "5.	f(x) = log x<BR>\n" );
document.write( "So, put x=1,2,4,8,16 and find the value of f(x)\r<BR>\n" );
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document.write( "f(1) = log(1) = 0<BR>\n" );
document.write( "f(2) = log(2) = 0.301<BR>\n" );
document.write( "f(4) = log(4) = 0.602<BR>\n" );
document.write( "f(8) = log(8) = 0.903<BR>\n" );
document.write( "f(16) = log(16) = 1.204\r<BR>\n" );
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document.write( "So, as the value of x increases, f(x) also increases. But the increase is very less in value compared to the above functions.<BR>\n" );
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