Interpret f(a+h)-f(a)/h on a graph of f(x)=√(x-1), h≥0 and a=2

Question

I don't really understand what this means?

Answer 1

To answer this question really takes a picture and, unfortunately, this answer space does not allow enough memory usage to paste in that picture.

Note that h is just some arbitrary number added to the x value of 2.

f(a+h)-f(a)/h, or in this case f(2+h)-f(2)/h (since a = 2), is just the slope of the secant line connecting the point where x = 2 (and y = 1) to the point where x = 2 + h and y = f(2+h).

It's nothing more than delta y divided by delta x.