Question 182277: 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.
1. f(x) = 2x – 5
2. f(x) = x2 - 4x + 3
3. f(x) = x3 + 4x2 - 2x - 3
4. f(x) = 7x
5. f(x) = log x
Answer by mastermath(14)   (Show Source):
You can put this solution on YOUR website! 1. f(x) = 2x – 5
So, put x=1,2,4,8,16 and find the value of f(x)
f(1) = 2(1) - 5 = 2 - 5 = -3
f(2) = 2(2) - 5 = 4 - 5 = -1
f(4) = 2(4) - 5 = 8 - 5 = 3
f(8) = 2(8) - 5 = 16 - 5 = 11
f(16) = 2(16) - 5 = 32 - 5 = 27
So, as the value of x increases, f(x) also increases.
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2. f(x) = x2 - 4x + 3
So, put x=1,2,4,8,16 and find the value of f(x)
f(1) = (1)^2 - 4(1) + 3 = 1 - 4 + 3 = 0
f(2) = (2)^2 - 4(2) + 3 = 4 - 8 + 3 = -1
f(4) = (4)^2 - 4(4) + 3 = 16 - 16 + 3 = 3
f(8) = (8)^2 - 4(8) + 3 = 64 - 32 + 3 = 35
f(16) = (16)^2 - 4(16) + 3 = 256 - 64 + 3 = 195
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.
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3. f(x) = x3 + 4x2 - 2x - 3
So, put x=1,2,4,8,16 and find the value of f(x)
f(1) = (1)^3 - 4(1)^2 -2(1) - 3 = 1 - 4(1) -2 - 3 = 1 - 4 - 5 = -8
f(2) = (2)^3 - 4(2)^2 -2(2) - 3 = 8 - 4(4) -4 - 3 = 8 - 16 - 7 = -15
f(4) = (4)^3 - 4(4)^2 -2(4) - 3 = 64 - 4(16) -8 - 3 = 64 - 64 - 11= -11
f(8) = (8)^3 - 4(8)^2 -2(8) - 3 = 512 - 4(64) -16 - 3 = 512 - 256 - 19 = 237
f(16) = (16)^3 - 4(16)^2 -2(16) - 3 = 4096 - 4(256) -32 - 3 = 4096 - 1024 - 35 = 3037
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.
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4. f(x) = 7x
So, put x=1,2,4,8,16 and find the value of f(x)
f(1) = 7(1) = 7
f(2) = 7(2) = 14
f(4) = 7(4) = 28
f(8) = 7(8) = 56
f(16) = 7(16) = 112
So, as the value of x increases, f(x) also increases.
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5. f(x) = log x
So, put x=1,2,4,8,16 and find the value of f(x)
f(1) = log(1) = 0
f(2) = log(2) = 0.301
f(4) = log(4) = 0.602
f(8) = log(8) = 0.903
f(16) = log(16) = 1.204
So, as the value of x increases, f(x) also increases. But the increase is very less in value compared to the above functions.
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