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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