Question 75490: This is a practice question for me so I know the answer but how do I work this?
Let f(x) = 5x-2.
Find:
(a) f(4) – f(3) Answer is: 5
(b) f(9) – f(8) Answer is: 5
(c) f(12) – f(11) Answer is: 5
(d) How do the results of (a) through (c) compare to the slope of the line that is the graph of f? Answer is: same
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! The way you solve these problems is just replace the x in the function with the number given.
a) If f(x) = 5x-2, find:
f(4)-f(3)
First, to find out what f(4) is, you replace x with 4 in the function f(x) = 5x-2, so:
f(4) = 5(4)-2
f(4) = 20-2
f(4) = 18
Similarly for f(3)
f(3) = 5(3)-2
f(3) = 15-2
f(3) = 13
Now, f(4)-f(3) = 18-13 = 5
b) For f(9)-f(8)
f(9) = 5(9)-2
f(9) = 45-2
f(9) = 43
Similiarly for f(8)
f(8) = 5(8)-2
f(8) = 40-2
f(8) = 38
Now, f(9)-f(8) = 43-38 = 5
You should get the picture by now.
d) The given function can be written as an equation in the slope-intercept form: y = mx+b where m is the slope and b is the y-intercept.
Your function can be similarly written:
y = 5x-2 where the slope m = 5 and the y-intercept, b = -2
So you can see that the slope of the given function is the same as the the differences given by:
f(x)-f(x-1)
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