college algebraplease
posted by ladybug on .
I am not understanding this question and I have read the chapter many times. Please help.
given the function of f(x)=4x8
a. find the the rate of change between the stated values for x:5 to 7
b. find the equation of a secant line containing the given points (5,f(5)), and (7,f(7))
Like I said I have no clue. Can you please show me how you got the answer please?

rate of change is (change in y)/(change in x)
f(5) = 12
f(7) = 20
y changes from 12 to 20 as x changes from 5 to 7:
rate of change is thus (2012)/(75) = 8/2 = 4
Note that the rate of change is the same as the slope of the line f(x)=4x8
The secant line is thus the line from (5,12) to (7,20). Or, it is the line from (5,12) with a slope of 4. Either way, you get
(y12) = 4(x5)
y = 4x 8
This is not surprising, since the secant joining any two points on a line is just a section of the same line.
It strikes me as odd that such a problem is posed. Could it be that the function is
f(x) = 4^x8. Probably not, as the values of f(x) would be quite large.
Oh well, if the function is wrong, just use the method above to find the secant.