## (Section 22)

We will use the graphing calculator to explore the local and global behavior of a function.  By local behavior, we mean what happens to the y-values as we stay very close to a particular x value?

 Enter the equation in your calculator and view it in a Zoom 4. Decimal window. Let's study this function near zero. First, you know this function has no function value at zero because of the x in the denominator. Therefore, even though the function appears to have a value at x=0, there is really a hole in the function when the function is near x = 0.  So look at the graph with the axes turned off.  (2nd Format (zoom)).  Notice there is a whole in the function where the y-axis would have crossed. What value is the function skipping over? There are two ways to study this.  First let's look at a set of table values in a small window around x=0.  Let the Tablemin= -.4 and Notice that all the y-values are staying very close to 1.  Therefore we could say that the point the function is skipping over is (0,1).  This could also be viewed by tracing on the function when x is very close to zero. What does this function do when x gets very large positively or negatively. To do this you might pick windows with higher values like 100