Determine the average rate of change of the function between the given values of the variable.

I suspect sally1 is expecting this to be taken just a little further, so taking up where Melody left off:

(f(a+h) - f(a))/h = (7/(a+h) - 7/a)/h

                        = (7a - 7(a+h))/(a*(a+h)*h) 

                        = -7h/(a*(a+h)*h)

                        = -7/(a*(a+h))

If t is on the horizinal axis and f(t) is on the vertical axis (which is normal)

f(t) = 7/t;    t = a, t = a + h

f(a)=7/a

f(a+h)=7/(a+h)

The time difference between time=a and time=a+h is a+h-a=h (this is the horizonal difference)

f(a+h)-f(a) is the vertical difference

the average rate of change of the function is the

(difference between the function values at the end points)/(difference in time)

Like speed = distance/time OR

like the gradient of a line where A and B are two point on the line

=(difference between the y values  /difference in the x values )

Average rate of change= [f(a+h)-f(a)]/h

I am confused. Why aren't there any numbers or letters?

Because you were only given a's and h's .

would you like me to make up some numbers? (only joking)

would you like me to try and draw you a graph?

It keeps coming up as incorrect. That's why I am so confused. But I do understand how you got your answer...because there isn't anything else left.

This  is the introduction to calculus

See if this picture helps

what does your answer come up as?

Its a mystery.............

Alan's answer was correct. So I suppose I put both your answer and his answer together?

Yes that is correct - Alan manipulated my answer to get the simplified answer that you wanted.