World 2-1 Functions, Relations, Domain and Range.

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Presentation transcript:

World 2-1 Functions, Relations, Domain and Range

Recall that a FUNCTION takes 1 input and produces only 1 output for that exact input. Mr. Function A RELATION, takes 1 input, but may produce multiple outputs for that given input. Ms. Relation Function Notation f(x) = 4x +10 output input (x, f(x) )

(1) Graph - Vertical Line Test Function ____ Function _____ A vertical line touches the curve at ONLY 1 spot at a time YES NO A vertical line touches MORE THAN 1 spot at a time. Function Relation

(2) Table of Values Each x value has only ONE y value. An x value has MORE THAN ONE y value x y x y Function ____ YES Function ____ NO Function Relation

(3) Mapping Diagram YES NO Function ____ AB f SourceTarget Each source value has only ONE target value Function ____ AB r A source value has MORE THAN ONE target value Function Relation

Ex. 1 Calculate the output value of each function

Not every x value can be inputted into a function. For example, Orange YES Brick NO x yx y x y you cannot input a value that will force the function to take a square root of a negative or divide by zero. Asymptote x y

DOMAIN: The set of all possible x values that can be inputted into a function RANGE: The set of all possible y values that are outputted from a function. x greater than 5 x less than or equal to 10 y is between 0 and 100 z is at most 50 INTERVAL NOTATIONSET BUILDER NOTATION x is 5, 6 or 7

(4,4) (-5,-2) Ex. 2 Determine the domain and range (0,0) D: _________ R: _________ D: _________ R: _________

Domain and Range Challenge

1. Find the Domain and Range D: ___________ R: ___________ [-6,5] [1,6]

2. Find the Domain and Range Domain: ___________ Range: ___________ [-8,6[ ]-4,5]

3. Find the Domain and Range Domain: ___________ Range: __________ ]-∞, ∞[ [-1, ∞[

4. Find the Domain and Range D: ___________ R: ___________ [-1, ∞[ ] -∞, ∞[

5. Find the Domain and Range D: ___________ R: ___________ ]-6, 6[ ] -5, 5[

6. Find the Domain and Range D: _______________ R: ___________ [-∞, 0[ U ]0, ∞[ ] 0, ∞[

7. Find the Domain and Range D: ___________ R: ___________ {1,3,5} {4,5,6}

Homework World 2-1 Homework