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World 2-1Functions, Relations, Domain and Range
Recall that a FUNCTION takes 1 input and produces only 1 outputfor that exact input.
Mr. Function
A RELATION, takes 1 input, butmay produce multiple outputs forthat 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
0 2
1 4
3 6
5 8
x y
1 0
2 1
4 3
4 5
Function ____YES Function ____NO
Function
Relation
(3) Mapping Diagram
YES NOFunction ____
A Bf
2
3
5
7
4
6
10
14
Source Target
Each source value has only ONE target value
Function ____
A Br
2
3
5
7
4
6
10
11
A source value has MORE THAN ONE target value
FunctionRelation
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
-4 0
0 2
5 3
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
1 6
2 3
3 2
6 1
-1 -6
-2 -3
-3 -2
-6 -1
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 NOTATION SET 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