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

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

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.

Functions and Graphs Part One: Vocabulary

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

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.

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.

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

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).

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?

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?

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.

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)

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}

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)

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

Get your clickers ready! Closure Get your clickers ready!

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

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

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

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

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

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