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

[f(x+h) – f(x)]/h

This is a concept that is at the heart of calculus (MAT1475 here at CityTech), which is why we’re studying it in precalculus. We haven’t yet discussed what the difference quotient represents. I’ll discuss it as some point, but the idea is basically contained in this graph:

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

But for now, you should focus on calculating and simplifying the difference quotient of a given function. In addition to the examples we did in class and the examples in the book, here are a couple video examples by PatrickJMT: