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. 2. f(x)

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. 2. f(x)      Log On


   

Question 156294: 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.
2. f(x) = x2 - 3x + 2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 2


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


y=x%5E2-3x%2B2 Start with the given equation.


y=%281%29%5E2-3%281%29%2B2 Plug in x=1.


y=1%281%29-3%281%29%2B2 Square 1 to get 1.


y=1-3%281%29%2B2 Multiply 1 and 1 to get 1.


y=1-3%2B2 Multiply -3 and 1 to get -3.


y=0 Combine like terms.


So if x=1, then y=0.

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


y=x%5E2-3x%2B2 Start with the given equation.


y=%282%29%5E2-3%282%29%2B2 Plug in x=2.


y=1%284%29-3%282%29%2B2 Square 2 to get 4.


y=4-3%282%29%2B2 Multiply 1 and 4 to get 4.


y=4-6%2B2 Multiply -3 and 2 to get -6.


y=0 Combine like terms.


So if x=2, then y=0.

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


y=x%5E2-3x%2B2 Start with the given equation.


y=%284%29%5E2-3%284%29%2B2 Plug in x=4.


y=1%2816%29-3%284%29%2B2 Square 4 to get 16.


y=16-3%284%29%2B2 Multiply 1 and 16 to get 16.


y=16-12%2B2 Multiply -3 and 4 to get -12.


y=6 Combine like terms.


So if x=4, then y=6.

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


y=x%5E2-3x%2B2 Start with the given equation.


y=%288%29%5E2-3%288%29%2B2 Plug in x=8.


y=1%2864%29-3%288%29%2B2 Square 8 to get 64.


y=64-3%288%29%2B2 Multiply 1 and 64 to get 64.


y=64-24%2B2 Multiply -3 and 8 to get -24.


y=42 Combine like terms.


So if x=8, then y=42.

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


y=x%5E2-3x%2B2 Start with the given equation.


y=%2816%29%5E2-3%2816%29%2B2 Plug in x=16.


y=1%28256%29-3%2816%29%2B2 Square 16 to get 256.


y=256-3%2816%29%2B2 Multiply 1 and 256 to get 256.


y=256-48%2B2 Multiply -3 and 16 to get -48.


y=210 Combine like terms.


So if x=16, then y=210.

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





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Table of Values:





xy
10


20


46


842


16210



Because the function is a quadratic, this means that the polynomial undergoes quadratic growth. This is faster than linear growth.