Question 173000: How do I evaluate the functions for the values of x given as 1, 2, 4, 8, and 16 and then describe the differences in the rate at which each function changes with increasing values of x? This is like totally a different language for me, please help!!!!
1. f(x) = 5x - 3
2. f(x) = x2 - 3x + 2
3. f(x) = 2x3 + 7x2 - x - 1
4. f(x) = 10x
5. f(x) = ln x
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! How do I evaluate the functions for the values of x given as 1, 2, 4, 8, and 16 and then describe the differences in the rate at which each function changes with increasing values of x?
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I'll do the 1st two. Use the same procedure to do the others.
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1. f(x) = 5x - 3
f(1) = 5*1-3 = 2 gives point (1,2)
f(2) = 5*2-3 = 7 gives point (2,7)
f(4) = 5*4-3 =17 gives point (4,17)
f(8) = 5*8-3 =37 gives point (8,37)
f(16)=5*16-3 =77 gives point (16,77)
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Find the slope between successive points:
(7-2)/(2-1) = 5
(17-7)/(4-2) = 10/2 = 5
(37-17)/(8-4) = 20/4 = 5
(77-37)/(16-8) = 40/8 = 5
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2. f(x) = x^2 - 3x + 2
f(1) = 1 -3 + 2 = 0 gives point (1,0)
f(2) = 4 -6 + 2 = 0 gives point (2,0)
f(4) = 16 -12 + 2 = 6 gives point (4,6)
f(8) = 64 -24 + 2 = 42 gives point (8,42)
f(16)= 256-48+2 = 210 gives point (16,210)
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Find the slope between successive points:
(0-0)/(2-1) = 0/1 = 0
(6-0)/(4-2) = 6/2 = 3
(42-6)/(8-4) = 36/4 = 9
(210-42)/(16-8) = 168/8 = 21
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Cheers,
Stan H.
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