HAPPY MONDAY. 1. Pick up your Builder and Weekly. 2 HAPPY MONDAY! 1. Pick up your Builder and Weekly. 2. Turn in Builder to tray at the door. 3. Write your weekly agenda in your planner. 4. Please complete the NEXT two sections of your SKILL BUILDER.

What is a function?

How would you use your calculator to solve 52? Input Output Press: 5 x2 25 The number you entered is the input number (or x-value on a graph). The result is the output number (or y-value on a graph). The x2 key illustrates the idea of a function.

Graph Equation Table of values A set of ordered pairs Mapping A function is a relation that gives a single output number for every valid input number. A relation is a rule that produces one or more output numbers for every valid input number. There are many ways to represent relations: Graph Equation Table of values A set of ordered pairs Mapping These are all ways of showing a relationship between two variables.

A function is a rule that gives a single output number for every valid input number. To help remember & understand the definition: Think of your input number, usually your x-coordinate, as a letter. Think of your output number, usually your y-coordinate, as a mailbox.

A function is a rule that gives a single output number for every valid input number. Input number Output number Can you have one letter going to two different mail boxes? Not a FUNCTION

A function is a rule that gives a single output number for every valid input number. Input number Output number Can you have two different letters going to one mail box?

Is this a function? Function x y 1 2 3 4 x y 5 6 7 5 6 7

Is this a function? Not a Function! x y x y 5 6 1 7 1 6 1 2 5 6 7

Is this a function? x y Not a function! 5 6 8 11 1 2 3 x y 5 6 11 8

These all represent the SAME function! In words: Double the number and add 3 As an equation: y = 2x + 3 These all represent the SAME function! As a table of values: x y -2 -1 -1 1 0 3 1 5 As a set of ordered pairs: (-2, -1) (-1,1) (0,3) (1, 5) (2, 7) (3, 9)

YES Example 1 Is this a function? Hint: Look only at the x-coordinates :00 Is this a function? Hint: Look only at the x-coordinates YES

NO Example 2 Is this a function? Hint: Look only at the x-coordinates :40 Example 2 Is this a function? Hint: Look only at the x-coordinates NO

Choice 1 Example 3 Choice One Choice Two :40 Example 3 Which mapping represents a function? Choice One Choice Two 3 1 –1 2 2 –1 3 –2 Choice 1

Example 4 Which mapping represents a function? A. B. B

Vertical Line Test Vertical Line Test: a relation is a function if a vertical line drawn through its graph, passes through only one point. AKA: “The Pencil Test” Take a pencil and move it from left to right (–x to x); if it crosses more than one point, it is not a function

Vertical Line Test Would this graph be a function? YES

Vertical Line Test Would this graph be a function? NO

X Y Relation (a set of ordered pairs) x -3 -1 1 y -7 2 -5 4 x y A FUNCTION is a relation in which each first value is paired with one and ONLY ONE second value. Relation (a set of ordered pairs) Input-Output Tables x -3 -1 1 y -7 2 -5 4 x y ( 1 , 2 ) ( 3 , 4 ) ( 1 , -1 ) ( 4 , 6 ) ( 6 , 8 ) Decide whether the relation is a function. Yes or No Why or why not? ____________________ x y -2 1 3 2 5 4 7 6 9 Decide whether the relation is a function. Yes or No Why or why not? _______________________ Vertical Line Test for Functions: a VERTICAL line crosses only one point on the graph Mapping Decide whether the relation is a function. Yes or No Why or why not? ______________ X Y Decide whether the relation is a function. Yes or No Why or why not? _______________ 8 12 16 11 13 17 -9