document.write( "Question 156295: 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
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\n" ); document.write( "3. f(x) = 2x3 + 7x2 - x - 1 \r
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Algebra.Com's Answer #115097 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
# 3\r
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\n" ); document.write( "\n" ); document.write( "Let's find the function value when $\"x=1\"$ :\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2x%5E3%2B7x%5E2-x-1\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%281%29%5E3%2B7%281%29%5E2-1-1\"$ Plug in $\"x=1\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%281%29%2B7%281%29%5E2-1-1\"$ Cube $\"1\"$ to get $\"1\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%281%29%2B7%281%29-1-1\"$ Square $\"1\"$ to get $\"1\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%2B7%281%29-1-1\"$ Multiply $\"2\"$ and $\"1\"$ to get $\"2\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%2B7-1-1\"$ Multiply $\"7\"$ and $\"1\"$ to get $\"7\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=7\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=1\"$ , then $\"y=7\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Let's find the function value when $\"x=2\"$ :\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2x%5E3%2B7x%5E2-x-1\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%282%29%5E3%2B7%282%29%5E2-2-1\"$ Plug in $\"x=2\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%288%29%2B7%282%29%5E2-2-1\"$ Cube $\"2\"$ to get $\"8\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%288%29%2B7%284%29-2-1\"$ Square $\"2\"$ to get $\"4\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=16%2B7%284%29-2-1\"$ Multiply $\"2\"$ and $\"8\"$ to get $\"16\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=16%2B28-2-1\"$ Multiply $\"7\"$ and $\"4\"$ to get $\"28\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=41\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=2\"$ , then $\"y=41\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Let's find the function value when $\"x=4\"$ :\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2x%5E3%2B7x%5E2-x-1\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%284%29%5E3%2B7%284%29%5E2-4-1\"$ Plug in $\"x=4\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%2864%29%2B7%284%29%5E2-4-1\"$ Cube $\"4\"$ to get $\"64\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%2864%29%2B7%2816%29-4-1\"$ Square $\"4\"$ to get $\"16\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=128%2B7%2816%29-4-1\"$ Multiply $\"2\"$ and $\"64\"$ to get $\"128\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=128%2B112-4-1\"$ Multiply $\"7\"$ and $\"16\"$ to get $\"112\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=235\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=4\"$ , then $\"y=235\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Let's find the function value when $\"x=8\"$ :\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2x%5E3%2B7x%5E2-x-1\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%288%29%5E3%2B7%288%29%5E2-8-1\"$ Plug in $\"x=8\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%28512%29%2B7%288%29%5E2-8-1\"$ Cube $\"8\"$ to get $\"512\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%28512%29%2B7%2864%29-8-1\"$ Square $\"8\"$ to get $\"64\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1024%2B7%2864%29-8-1\"$ Multiply $\"2\"$ and $\"512\"$ to get $\"1024\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1024%2B448-8-1\"$ Multiply $\"7\"$ and $\"64\"$ to get $\"448\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1463\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=8\"$ , then $\"y=1463\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Let's find the function value when $\"x=16\"$ :\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2x%5E3%2B7x%5E2-x-1\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%2816%29%5E3%2B7%2816%29%5E2-16-1\"$ Plug in $\"x=16\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%284096%29%2B7%2816%29%5E2-16-1\"$ Cube $\"16\"$ to get $\"4096\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%284096%29%2B7%28256%29-16-1\"$ Square $\"16\"$ to get $\"256\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=8192%2B7%28256%29-16-1\"$ Multiply $\"2\"$ and $\"4096\"$ to get $\"8192\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=8192%2B1792-16-1\"$ Multiply $\"7\"$ and $\"256\"$ to get $\"1792\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=9967\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=16\"$ , then $\"y=9967\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now let's make a table of the values we just found.\r
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Table of Values:

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document.write( "x y
1 7
2 41
4 235
8 1463
16 9967\r\n" );
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\n" ); document.write( "\n" ); document.write( "Since this polynomial is a cubic, this tells us that the rate of growth is cubic growth. This growth rate is larger than quadratic growth.\r
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