Assignment #1

Exploring Equations of the Form by Mark Cowart (EMT668/Summer 1998)

Equations of the form yield some interesting graphs and enable students to form generalizations about the graph of the equation when n is positive or negative, or large or small, or possibly negative or a fraction. Furthermore, students can gain experience using Algebra Xpressor, Graphing Calculator 2.0, or any of the TI 80 series calculators while exploring quickly and efficiently several graphs of these particular equations.

Graph the following equations. Sketch each graph and look for any patterns. Discuss your findings and make some generalizations about the graphs of 1) 2) 3) 4) 5) 6) Click here for the graphs of several of these equations (for you to compare).

Why do you think even powers of the n exponent approach the graph of a square as n increases? What about odd powers?

Create some more equations of the general form of your own. Describe what happens if the exponent, n, is negative or a fraction. Explore several possibilities and make some generalizations.