SOLUTION: 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. 3. f

Algebra ->  Graphs -> SOLUTION: 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. 3. f      Log On


   

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.

3. f(x) = 2x3 + 7x2 - x - 1


Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 3

Let's find the function value when x=1:


y=2x%5E3%2B7x%5E2-x-1 Start with the given equation.


y=2%281%29%5E3%2B7%281%29%5E2-1-1 Plug in x=1.


y=2%281%29%2B7%281%29%5E2-1-1 Cube 1 to get 1.


y=2%281%29%2B7%281%29-1-1 Square 1 to get 1.


y=2%2B7%281%29-1-1 Multiply 2 and 1 to get 2.


y=2%2B7-1-1 Multiply 7 and 1 to get 7.


y=7 Combine like terms.


So if x=1, then y=7.

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Let's find the function value when x=2:


y=2x%5E3%2B7x%5E2-x-1 Start with the given equation.


y=2%282%29%5E3%2B7%282%29%5E2-2-1 Plug in x=2.


y=2%288%29%2B7%282%29%5E2-2-1 Cube 2 to get 8.


y=2%288%29%2B7%284%29-2-1 Square 2 to get 4.


y=16%2B7%284%29-2-1 Multiply 2 and 8 to get 16.


y=16%2B28-2-1 Multiply 7 and 4 to get 28.


y=41 Combine like terms.


So if x=2, then y=41.

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Let's find the function value when x=4:


y=2x%5E3%2B7x%5E2-x-1 Start with the given equation.


y=2%284%29%5E3%2B7%284%29%5E2-4-1 Plug in x=4.


y=2%2864%29%2B7%284%29%5E2-4-1 Cube 4 to get 64.


y=2%2864%29%2B7%2816%29-4-1 Square 4 to get 16.


y=128%2B7%2816%29-4-1 Multiply 2 and 64 to get 128.


y=128%2B112-4-1 Multiply 7 and 16 to get 112.


y=235 Combine like terms.


So if x=4, then y=235.

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Let's find the function value when x=8:


y=2x%5E3%2B7x%5E2-x-1 Start with the given equation.


y=2%288%29%5E3%2B7%288%29%5E2-8-1 Plug in x=8.


y=2%28512%29%2B7%288%29%5E2-8-1 Cube 8 to get 512.


y=2%28512%29%2B7%2864%29-8-1 Square 8 to get 64.


y=1024%2B7%2864%29-8-1 Multiply 2 and 512 to get 1024.


y=1024%2B448-8-1 Multiply 7 and 64 to get 448.


y=1463 Combine like terms.


So if x=8, then y=1463.

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Let's find the function value when x=16:


y=2x%5E3%2B7x%5E2-x-1 Start with the given equation.


y=2%2816%29%5E3%2B7%2816%29%5E2-16-1 Plug in x=16.


y=2%284096%29%2B7%2816%29%5E2-16-1 Cube 16 to get 4096.


y=2%284096%29%2B7%28256%29-16-1 Square 16 to get 256.


y=8192%2B7%28256%29-16-1 Multiply 2 and 4096 to get 8192.


y=8192%2B1792-16-1 Multiply 7 and 256 to get 1792.


y=9967 Combine like terms.


So if x=16, then y=9967.

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Now let's make a table of the values we just found.



Table of Values:





xy
17


241


4235


81463


169967


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.