Calculus Fall 2010 Lesson 01
Lesson Plan #015
Class: Precalculus Date: Friday October 5th, 2012
Topic: Analyzing graphs of functions. Aim: How can we analyze the graphs of functions?
Objectives:
1) Students will be able to analyze the graphs of functions
HW# 015: Page 88 #’s58, 64, 74, 82, 88, 102, 112, 114, 120, 124
Do Now:
Sketch the graph of [pic]in the interval [pic]
PROCEDURE:
Write the Aim and Do Now
Get students working!
Take attendance
Give back HW
Go over HW
Go over the Do Now
Assignment #1:
Example:
Find the minimum and maximum values of the function [pic]in the interval [pic]
Example:
Find the minimum and maximum values of the function [pic] in the interval[pic].
Assignment #2:
Looking at the graph at right, for what value(s) x value do we have a maximum for this function?
Looking at the graph at right, for what value(s) of x value do we have a maximum for this function?
Assignment #3:
Determine from the graph whether or not [pic]possesses a minimum on the given interval (a,b)
A) B)
Assignment #4:
Does the function at right have a minimum in the interval[pic]?
Does the function at right have a maximum in the interval[pic]?
For this function, is there an open interval for which there is a maximum or minimum?
Let’s check out this website for a better understanding of relative extrema.
Online Activity:
Let’s go to to look at a variety of examples illustrating absolute extrema and relative extrema.
Assignment #5:
Let’s use the graphing calculator to identify the x-values of relative extrema.
Enter the equation [pic]
While some functions are defined by single formulas, others are defined by applying different formulas to different parts of their domains. For example:
DEFINITION. A piecewise defined function is a function which is defined symbolically using two or more formulas.
Assignment #6:
Sketch the graph of each piece wise defined function.
A) [pic] B) [pic]
Assignment #7: Sketch the graph of the piece-wise defined function below
[pic]
For the above function, evaluate
A)
B) [pic][pic]
Sketch the graph of the piecewise function defined above
Let’s graph a piecewise defined function on the graphing calculator. To graph the piecewise defined function from above press the Y= button, enter the following data into your graphing calculator in the Y= section
(X2-1)(X ................
................
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