Laboratory I.2
Functions and Their Graphs
Goals
• The student will become more familiar with graphing functions in DERIVE
• The student will gain more experience doing algebra with DERIVE.
In the lab (80 pts)
In the first part of this lab, we will explore some functions using DERIVE and its ability
to do algebra and graphing. In the second part, we will use DERIVE to explore a scenario and
see how functions are used in that exploration. The instructions in the second part will be less
explicit on how to use since you will have learned what you need in the first part.
You should
read through the lab and answer the "Ready for Lab?" questions. You must turn these in
at the beginning of the lab session, to be allowed to turn in the rest of the lab.
Note:
This document is for use with DERIVE v. 6.0.
To check if you are using the correct
version of DERIVE, go to the Help:About Derive menu.
If you are using an earlier version,
please see the instructor on starting v. 6.0.
1.
In this first example, you will use DERIVE to compare interpreting the graph of a function to
solving for intercepts algebraically.
Author
f(x) := x^3  5x^2  x + 5
and plot it (pay close attention to the colon
before the equal sign). Make a note of the
x
intercepts. Check to see if you have all the
x

intercepts by solving the equation
f
(
x
) = 0 .To do this, get back to the algebra window,
Author
f(x) = 0
(here we should not use a colon before the equal sign)., and push
Solve
button and
then click on Solve option. Did you find another intercept? Go back to the graph and zoom out to
include all intercepts. When you get the graph right, use File: Embed or CtrlB to copy it in the
Algebra Window.
Use DERIVE to solve the inequality
f
(
x
) < 0. You are going to need this to answer one question
in the After the Lab section.
You're going to want to start a fresh graph for the next problem. Go back to the plot window and
use
File:Close
(or
AltF:C
) to get rid of the old graph.
2.
In this example, you will review the features of a periodic function and determine whether
DERIVE uses degrees or radians by default.
Author
g(x) := sin(x)
and
Plot
it. Zoom in or out as needed. Is
x
measured in degrees or
radians? How could you tell? (Recall the period of the sine function is 2
π
radians or 360°.) Find
the
x
intercepts by solving
g
(
x
) = 0. Did DERIVE find all the
x
intercepts?
Next
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MATH 2413
Lab 2
Page 2 of 4
Author
h(x) := sin(x deg)
and plot it on a fresh graph. What is the period and what are
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 Spring '10
 Moody
 Trigonometry, Periodic function, Inverse function

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