## (Section 6)

##### What is a function?  Is it an equation?  Is it a picture?  Is it a graph?  Think for a few minutes about what you think you know about a function?

If a caterpillar is crawling around on a piece of graph paper, as shown below.  Your teacher asks you to determine the location of the creature on the graph paper at particular times.  Would you define the position of this caterpillar as a function of time?**

##### Now that you have cleared up your thinking about a function, let's return to our initial example.  What about the caterpillar?  This answer is a bit tricky. The catapillar's position can be thought of as a point (x,y).  Time is another variable.  Is the path of the caterpillar or position of the caterpillar,  a function of time?  Yes it is.  For every t value of time there is exactly one location for the caterpillar on the graph paper, even though the location probably is named with a coordinate (x,y).   You won't experience these types of functions until much later in your study of Calculus.  It is not usually part of a first two semesters of Calculus.  But you should know it is an example of a function.  You will also study some other types of graphs throughout the second semester of Calculus that will also challenge you to think carefully.  You will be studying parametric equations and polar equations.

1.  Tell whether each of the following is or is not a function

 a. b. c. d. e.

2.  Which of the following indicate that y is a function of x?

 a. b.  y = x/3 c.  xy = 8 d. e. f.

**Some of them material on functions is based on What do Students Really know about Functions? by Barbara Edwards and Karen Graham in the December, 2001 Mathematics Teacher)