Survey

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Survey

Document related concepts

Transcript

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. How would you use your calculator to solve 52? Input Press: 5 Output x2 25 The number you entered is the input number (or x-value on a graph). The result is the output number (or yvalue on a graph). The x2 key illustrates the idea of a function. 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? x 1 2 3 4 y 5 6 7 Function x 1 2 3 4 y 5 6 7 6 Is this a function? Not a Function! x 1 y 5 6 2 7 x 1 2 1 1 y 5 6 7 6 Is this a function? x y 1 5 2 6 3 8 11 Not a function! x 1 2 2 3 y 5 6 11 8 In words: Double the number and add 3 As an equation: y = 2x + 3 As a table of values: x y -2 -1 -1 1 0 3 1 5 These all represent the SAME function! As a set of ordered pairs: (-2, -1) (-1,1) (0,3) (1, 5) (2, 7) (3, 9) Example 1 {(0, 5), (1, 4), (2, 3), (3, 2), (4, 1), (5, 0)} •Is this a function? •Hint: Look only at the x-coordinates YES Example 2 {(–1, 7), (1, 0), (2, 3), (0, 8), (0, 5), (–2, 1)} •Is this a function? •Hint: Look only at the x-coordinates NO Example 3 Which mapping represents a function? Choice One 3 1 0 –1 2 3 Choice Two 2 –1 3 Choice 1 2 3 –2 0 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 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) x y ( 1 , 2 ) Decide whether the relation ( 1 , -1 ) (4 , 6) -3 -1 0 -3 1 y -7 -3 2 -5 4 x y Why or why not? ____________________ -2 1 0 3 ____________________ 2 5 Why or why not? _______________________ ____________________ 4 7 _______________________ 6 9 _______________________ (6 , 8) Mapping 11 13 17 -9 x Yes or No is a function. (3 , 4) Input-Output Tables 8 12 16 Decide whether the relation is a function. Yes or No Why or why not? ______________ ______________ ______________ ______________ Decide whether the relation is a function. Yes or No Vertical Line Test for Functions: a VERTICAL line crosses only one point on the graph Decide whether the relation is a function. Yes or No Why or why not? _______________ _______________ _______________ _______________ Identifying Functions Name: ________________ Part A: Determining Function with Tables and Mappings Determine if each relation below is a function. 1. 2. Function: Y N Function: Y N 3. Function: Y N