1. Written by: Coryn Wilson Warren, Ohio
Functions
Vocabulary Part One
Written by: Coryn Wilson
Warren, Ohio

2. Instructor Notes
Subject Area(s): Math – Patterns, Functions and Algebra Standard
Grade level: 8
Lesson Length: about 40 minutes
Synopsis: This lesson is an introduction to a unit on functions. It introduces a lot of new vocabulary related to functions and graphs of functions.
Objective/goals:
Understand what a function is
Create a function table using input and output values
Differentiate between independent and dependent variables
Identify the relation, given a domain and range
Differentiate between continuous and discrete functions

3. Instructor Notes Standards: Patterns, Functions, and Algebra
Relate the various representations of a relationship; i.e., relate a table to graph, description and symbolic form
Extend the uses of variables to include covariants where y depends on x
Differentiate and explain types of changes in mathematical relationships, such as continuous vs. noncontinuous
Differentiate between discrete and continuous data and appropriate ways to represent each.
Pre-requisite skills: Students must be able to evaluate algebraic expressions, recognize and graph linear equations, and plot ordered pairs.
TurningPoint functions: Standard question slides
Materials: Classroom notes handout (attached)
*Instructional delivery notes can be found in the notes section of the slide.

4. Functions and Graphs
Part One: Vocabulary

5. Check Prior Knowledge Domain Dependent Variable Input
Take a look at these new vocabulary words. Do any of them look familiar? Which ones?
Domain
Dependent Variable
Input
Continuous Function
Independent Variable
What do you remember about these words?
Output
Function
Range
Discrete Function
Relation

6. Function
A function is a relationship between two values, an input and an output.
EXAMPLE: The world is full of these types of relationships, when one thing depends on another thing:
Buying new shoes depends on your parents having money. Your parents having money depends on their having a job. Your parents having a job depends on how well they do their job and on how well the company is doing financially.
Your grade in school is depends on how hard you work in school. How hard you work in school depends on your attitude toward school.
How good you are at a task- playing video games, dancing, or playing basketball- depends on how much time and effort you spend at doing it.

7. Why do we need to understand functions?
To understand how things work and make our lives better. Here are some examples of how functions affect your daily lives.
Understanding the relationship between gasoline, air, and fire is what makes a car go.
Understanding the relationship between heat and bacteria allows us to eat food safely.
Understanding that electrons flow from a positive pole to a negative pole allows us to have c.d. players, MP3 players, telephones, and televisions.

8. Input Vs. Output
Another way to understand a function is as a machine. A machine has an input and an output. There is a relationship that exists between the input and output. The output depends on the input. The machine receives the input and transforms it into the output.
Input
Machine
Output
bread
toaster
toast
dirty clothes
washer
clean clothes

9. Input Vs. Output
The input is the number that you plug into the function. It is also known as the independent variable (x).
The output is the number that you get after you perform the function. It is also known as the dependent variable (y).

10. Here’s an example of a function table. Does it look familiar?
Input (x)
Function
2x + 11
Output (y) 3
2(3) +11 17 6
2(6) + 11 23 -3
2(-3) + 11 ?
_____
2(____) + 11
Which value, the input or the output, do you have a choice on what to use?

11. Independent Vs. Dependent Variables
Independent Variable (x)- the variable within the function with a value that is subject to choice.
Dependent Variable (y)– the variable within the function that depends on the value of the independent variable
Your cell phone bill compared to how much you talk/text.
What are the independent and dependent variables?

12. Independent Vs. Dependent Variables
Your cell phone bill compared to how much you talk/text.
What are the independent and dependent variables?
Well, since the total cost depends on the amount you talk/text, the dependent variable is your bill and the independent variable is the amount of time you talk/text.

13. Relation What are the ordered pairs represented in this relation?
A relation is a set of ordered pairs
Think back to your cell phone bill. If you talk for 100 minutes, your bill is $10. If you talk for 500 minutes, your bill is 50$. If you talk for 1000 minutes, your bill is $100.
What are the ordered pairs represented in this relation?
(100, 10)
(500, 50)
(1000, 100)

14. Domain and Range What is the range of this relation?
The set of the first numbers (x) in the ordered pairs is the domain of the relation
The set of second numbers (y) of the ordered pairs is the range of the relation
Cell Phone Bill
What is the range of this relation?
What is the domain of this relation?
{10, 50, 100, 150}
{100, 500, 1000, 1500}

15. Discrete and Continuous Functions
Discrete Function – a function with a graph of unconnected points
Continuous Function – a function with a graph of connected points (a line or curve)

16. Important to Remember…
X-coordinate
Input
Independent Variable
Domain
Y-coordinate
Output
Dependent Variable
Range

17. Get your clickers ready!
Closure
Get your clickers ready!

18. A ____ is a relationship between input and output values.
Graph
Function
Independent Variable
Domain 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

19. All of the following refer to the first number in an ordered pair except…
Domain
Input
Dependent Variable
X-coordinate 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

20. Number of Calories burned Place you are walking to
The number of calories you burn increases as the number of minutes you walk increases. What is the independent variable for this situation?
Time
Number of Calories burned
Place you are walking to
Shoes you are wearing 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

21. Total cost of your purchase Number of games you buy
The total cost of your purchase depends on the number of games you buy. Identify the dependent variable.
Total cost of your purchase
Number of games you buy
The store you are at
The type of game you are buying 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

22. The graph at the right is an example of a _____ function.
Discrete
Independent
Range
Continuous 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

23. Make Flashcards Term (on one side)
Homework
Make Flashcards
Term (on one side)
Definition and Example (on other side)