Lesson Plan #6



Lesson Plan #2

Class: AP Calculus Date: Friday September 9th, 2011

Topic: Identifying Even and Odd Functions Aim: How do we identify even and odd functions?

Objectives:

1) Students will be able to determine if a function is even, odd or neither.

2) Students will be able to evaluate the value of a piecewise defined function for a specific value of the domain.

3) Students will be able to graph piecewise defined functions.

4) Students will be able to evaluate composite functions.

HW# 2:

1) a) Find the domain and range of the function [pic].

b) Draw the graph of the function in part a

c) Determine whether the function is even, odd or neither. 3) If [pic] and [pic],

[pic], [pic]

2) a) Sketch the graph of the piecewise function [pic] find [pic]

b) Evaluate f(0), f(1), f(2) [pic], [pic]

Do Now:

Examine the function f(x) = |x|.

Evaluate f(2), f(3), f(4), f(-2), f(-3), f(-4)

With respect to the above function, what is the relationship between f(x) and f(-x)?

A function f(x) is even if f(x)=f(-x)

Below are graphs of even functions. What is a characteristic of all 3 even functions graphed below?

Examine the function f(x) = x3.

Evaluate f(2), f(3), f(4), f(-2), f(-3), f(-4)

What relationship exists between f(x) and f(-x)?

A function f(x) is odd if f(-x)=-f(x).

Below are graphs of odd functions. What is a characteristic of all 3 odd functions graphed below?

PROCEDURE:

Write the Aim and Do Now

Get students working!

Take attendance

Go over the HW

Collect HW

Go over the Do Now

Assignment #1:

Determine whether the following functions are even, odd or neither:

A) [pic]

[pic]

B) [pic]

C) [pic][pic]

D) [pic]

E) [pic]

While some functions are defined by single formulas, others are defined by applying different formulas to different parts of their domains. For example:

[pic]

DEFINITION. A piecewise defined function is a function which is defined symbolically using two or more formulas.

[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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