**Chapter 3 (PDM)**

**Lesson Plan 3-1: Arithmetic
Operations on Functions**

__Content Standards and Benchmarks:__

I,2,3: Expand their understanding of functions to include non-linear functions, composition
of functions, inverses of functions, and piecewise and recursively defined functions.**
**

I,2,6:
Increase their use of functions and mathematical models to solve problems in context.

** **

__Objective:__

**
**After reading the lesson the night before, and
hearing my short lecture regarding arithmetic operations on functions, students will be able to use arithmetic operations
on functions to derive equations which model realistic situations.

Students will also be able to graph functions obtained from applying arithmetic operations
to the functions.

__Anticipatory Set:__

**Warm-up: NO CALCULATORS PLEASE!**

** Functions can do some ****CRAZY**** things! See what I mean?**

1. What is the shape
of the function that results when you add these two functions together?

f(x) = sin(x) and g(x) =.5x

2. If h(x) = f(x)g(x)
what are some properties of h(x) when f(x) = x and g(x)= sin x?

__Input__**: “This is what you need to know.”**

v Simplify arithmetically modified equations.

v Where is it defined/undefined?

**“Any questions?”**

** **

**Modeling:**

v Answer student questions from the night before.

v Tie in today’s objectives with the questions that are
asked.

**Guided Practice:**

v As the students get more comfortable with the content, I will ask them to lead me through
the problems.

v I may even ask student to come up to the board to do that other students are confused
about problems.

**Independent practice:**

v Students will be assigned lesson 3-2 to
read and do the C.A.R. problems for the next day.

**Closure:**

v **“If you could say there were three important things
to remember from today’s lesson, what would they be?”**

Ø
How
to add functions graphically

Ø
How
to add functions algebraically

Ø
Simplify
arithmetically synthesized

functions

Ø
Know
where the resulting function is defined and undefined