As we have discussed in class (and as you have seen in the homework!), the difference quotient of a function f(x) is defined as:

[f(x+h) – f(x)]/h

Why are we interested in the difference quotient? This is a concept that is at the heart of calculus (MAT1475 here at CityTech), which is why we are studying it in precalculus!

The idea behind the difference quotient is demonstrated by this graph:

(Hint: what’s the slope of the “secant line”?)