Precalculus, Lab 5: Power Functions

February 2, 2012

Introduction

In this lab, we will investigate the behavior of various kinds of power functions.  Print off the lab worksheet from the course website.  The lab worksheet has detailed instructions for the explorations as well as questions for you to answer.  Use this notebook for computations, but answer the questions (in paragraph form) on the worksheet.

Plot Commands

For the commands in this lab to work correctly, we need to tell Mathematica that we are interested in real numbers only (not complex numbers).  So the first thing to do is evaluate the following command.

Needs["Miscellaneous`RealOnly`"]

Place your cursor at the end of the line and press Shift+Enter.  Mathematica will tell you that the package is obsolete, but that’s okay.

For many of the exercises in this lab you will be plotting several functions on the same set of axes.  You can do this by giving the Plot command a list of functions (using curly braces) instead of just one function.  For example, this command will plot the functions y=x, y=(x^3),and y=(x^5) on the same set of axes:

Plot[{x,x^3,x^5},{x,-2.35,2.35},PlotRange->{-1.5,1.5}]

This is the only Mathematica command you need for this lab!  Just change the functions you are plotting and change the x-range and y-range according to the exercise you’re working on.