More preliminaries:  The Algebra of Functions.  For a more in-depth review, see the following pages from the PreCalculus class:

Chapter0501

Chapter0502

Chapter 0612

Chapter0613

For Calculus, it's important to draw your attention especially to the composition of functions (see the second link, above.)  Here's the applet that shows, graphically, the composition, g(f(x)), using the "reflect off the y = x line" trick, to simplify turning the output from "f" into the input for "g."

Applet

Here are a few worked examples, similar to the assigned problems in the homework:

Here's an applet that shows exactly what's going on for Problem #94, Section P3:

And finally, an example we'll come back to frequently, so I didn't bother assigning it (yet):

The "secant line" example from the previous section gives rise to what is known as a "difference quotient:"

Example:  Find the slope for the line through the function f(x) at the point "x" and the point x + delta_x (in the book and in the written example below, the triangle-x thingy is actually the Greek capital letter "delta."  Notice that "delta x" is a totally separate variable, NOT "delta times x."  That's one of the first confusions from the example.  Look at this page carefully, and we'll come back to it in chapters 1 and 2 and 3.

Now, try the homework from section P.3

Also, try Project #1

Next, Chapter 1