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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