Name: _____________________________________ Date: ________________ Block: _____ Functions New Vocab Algebra I – A.7: The student will investigate and analyze function families and their characteristics both algebraically and graphically, including a) determining whether a relation is a function; b) domain and range Relation – any pairing of a set of ____________ with a set of _____________. We will be talking a lot about relations as a group of __________________________. Function – a special kind of ______________ where each ______________ is paired with one and ONLY one ______________. Domain – the set of ______ ______ values (in an ordered pair, it is the _______________) Range – the set of _____________ values (in an ordered pair, it is the _______________) Independent Variable – the ____________ variable Dependent Variable – the _____________ variable Domain vs. Range Identify the domain and range of the functions: 1. Input (x) Output (y) 0 5 D: { R: { 1 2 2 2 4 1 } } 2. { (3, 1); (0, 2); (7, 2) } D: { R: { } } Domain vs. Range Identify the domain and range of the functions: 3. D: { R: { 4. D: { R: { } } 5. D: { R: { } } 0 4 2 5 Examples of relations and functions 2 3 Relations and functions can be represented in a few different ways: Let’s represent the following relation: { (-3, 2); (0, 5); (2, 4); (-1, 9) } Tables x Difference between a function and a relation } } Mapping Graph y Every _____________________ is a ____________________ , but not every ___________________ is a _____________________. The only way a relation is a function is that if for every input, _______________________ ___________________________________. Determine if the relation is a function 1. Function 5 2 3 - Examples: 3 6 or Not a function Why? _______________________________ ____________________________________ 1 Domain: Range: 2. Function or Not a function Why? _______________________________ ____________________________________ Domain: Range: 3. { (-3, 2); (0, 5); (2, 4); (-1, 9) } Function or Not a function Why? ______________________________ ____________________________________ Domain: Range: The Vertical Line Test An easy way to tell if graphs are functions is by using the _____________________. A relation on a graph is a ____________ if no vertical line passes through ______________________ on the graph. Examples of the Vertical Line Test Use the Vertical Line Test to determine whether each relation is a function: Independent and Dependent Variables 1. You are buying concert tickets that cost $15 each. If you buy 6 tickets, how much will it cost? Identify the independent and dependent variable. 2. Every 30 minutes that you exercise, you burn 200 calories. If you burned 1000 calories, how many minutes have you exercised? Identify the independent and dependent variable. 3. If you are traveling in a car at 50 miles per hour, and you are driving for 3 hours, how much distance have you traveled? Identify the independent and dependent variable. Practice ON A PIECE OF SCRATCH PAPER-- Use the following to: a) Determine whether the following are functions or just relations b) Find the domain and range x y -3 0 -2 2 1 2 4 5 6 9 1. 2. 3. 4. x -3 2 8 -3 y 1 5 2 0 5. Come up with a situation that involves an independent and dependent variable. Hint: Think of something that has a cause and effect!