Page 35 - Calculus Workbook For Dummies

Chapter 2

Funky Functions and Tricky Trig

In This Chapter
Figuring functions
Remembering Camp SohCahToa

n Chapter 2, you continue your pre-calc warm-up that you began in Chapter 1. If algebra is
Ithe language calculus is written in, you might think of functions as the “sentences” of cal-
culus. And they’re as important to calculus as sentences are to writing. You can’t do calculus
without functions. Trig is important not because it’s an essential element of calculus — you
could do most of calculus without trig — but because many calculus problems happen to
involve trigonometry.

Figuring Out Your Functions

To make a long story short, a function is basically anything you can graph on your graphing
calculator in “ y =” or graphing mode. The line y = 3 x - 2 is a function, as is the parabola
2
y = 4 x - 3 x + 6. On the other hand, the sideways parabola x = y 3 2 - y 4 + 6 isn’t a function
because there’s no way to write it as y = something. Try it.

You can determine whether or not the graph of a curve is a function with the vertical line test.
If there’s no place on the graph where you could draw a vertical line that touches the curve
more than once, then it is a function. And if you can draw a vertical line anywhere on the
graph that touches the curve more than once, then it is not a function.

As you know, you can rewrite the above functions using “f xh” or “g xh” instead of “y.” This
^
^
changes nothing; using something like f xh is just a convenient notation. Here’s a sampling
^
of calculus functions:
5
g x = 3 x - 20 x 3
l ^ h
x + h - x
x =
f l ^ h lim
h " 0 h
x
A x = # 10 dt
f ^ h
3
Virtually every single calculus problem involves functions in one way or another. So should
you review some function basics? You betcha.