find the average rate of change:
f(x)=7x-6
(a,f(a)) and (b,f(b))
Well, with calculus you can look at it and see 7 as the rate of change.
In precal,
avg rate= (f(b)-f(a))/(b-a)=(7b-6-7a+6)/(b-a)= 7 (b-a)/(b-a)=7
by inspection, f(x) is a linear function, with slope = 7
since the slope is constant, the average rate of change is just 7.
To find the average rate of change of a function, we need to determine the difference in the function values at two given points divided by the difference in their respective x-values.
In this case, we have the two points (a, f(a)) and (b, f(b)).
The formula for the average rate of change is:
Average Rate of Change = (f(b) - f(a)) / (b - a)
In our case, f(x) = 7x - 6, so we can substitute the values of f(a) and f(b) into the formula.
Average Rate of Change = ((7b - 6) - (7a - 6)) / (b - a)
Simplifying further:
Average Rate of Change = (7b - 7a) / (b - a)
Therefore, the average rate of change of the function f(x) = 7x - 6 between the points (a, f(a)) and (b, f(b)) is (7b - 7a) / (b - a).