World 2-1 Functions, Relations, Domain and Range.
-
Upload
lydia-wheeler -
Category
Documents
-
view
231 -
download
0
Transcript of World 2-1 Functions, Relations, Domain and Range.
![Page 1: World 2-1 Functions, Relations, Domain and Range.](https://reader035.fdocuments.in/reader035/viewer/2022062315/5697c0081a28abf838cc6e1a/html5/thumbnails/1.jpg)
World 2-1Functions, Relations, Domain and Range
![Page 2: World 2-1 Functions, Relations, Domain and Range.](https://reader035.fdocuments.in/reader035/viewer/2022062315/5697c0081a28abf838cc6e1a/html5/thumbnails/2.jpg)
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) )
![Page 3: World 2-1 Functions, Relations, Domain and Range.](https://reader035.fdocuments.in/reader035/viewer/2022062315/5697c0081a28abf838cc6e1a/html5/thumbnails/3.jpg)
(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
![Page 4: World 2-1 Functions, Relations, Domain and Range.](https://reader035.fdocuments.in/reader035/viewer/2022062315/5697c0081a28abf838cc6e1a/html5/thumbnails/4.jpg)
(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
![Page 5: World 2-1 Functions, Relations, Domain and Range.](https://reader035.fdocuments.in/reader035/viewer/2022062315/5697c0081a28abf838cc6e1a/html5/thumbnails/5.jpg)
(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
![Page 6: World 2-1 Functions, Relations, Domain and Range.](https://reader035.fdocuments.in/reader035/viewer/2022062315/5697c0081a28abf838cc6e1a/html5/thumbnails/6.jpg)
Ex. 1 Calculate the output value of each function
![Page 7: World 2-1 Functions, Relations, Domain and Range.](https://reader035.fdocuments.in/reader035/viewer/2022062315/5697c0081a28abf838cc6e1a/html5/thumbnails/7.jpg)
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
![Page 8: World 2-1 Functions, Relations, Domain and Range.](https://reader035.fdocuments.in/reader035/viewer/2022062315/5697c0081a28abf838cc6e1a/html5/thumbnails/8.jpg)
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
![Page 9: World 2-1 Functions, Relations, Domain and Range.](https://reader035.fdocuments.in/reader035/viewer/2022062315/5697c0081a28abf838cc6e1a/html5/thumbnails/9.jpg)
(4,4)
(-5,-2)
Ex. 2 Determine the domain and range
(0,0)
D: _________
R: _________
D: _________
R: _________
![Page 10: World 2-1 Functions, Relations, Domain and Range.](https://reader035.fdocuments.in/reader035/viewer/2022062315/5697c0081a28abf838cc6e1a/html5/thumbnails/10.jpg)
Domain and Range Challenge
![Page 11: World 2-1 Functions, Relations, Domain and Range.](https://reader035.fdocuments.in/reader035/viewer/2022062315/5697c0081a28abf838cc6e1a/html5/thumbnails/11.jpg)
1. Find the Domain and Range
D: ___________ R: ___________[-6,5] [1,6]
![Page 12: World 2-1 Functions, Relations, Domain and Range.](https://reader035.fdocuments.in/reader035/viewer/2022062315/5697c0081a28abf838cc6e1a/html5/thumbnails/12.jpg)
2. Find the Domain and Range
Domain: ___________ Range: ___________[-8,6[ ]-4,5]
![Page 13: World 2-1 Functions, Relations, Domain and Range.](https://reader035.fdocuments.in/reader035/viewer/2022062315/5697c0081a28abf838cc6e1a/html5/thumbnails/13.jpg)
3. Find the Domain and Range
Domain: ___________ Range: __________]-∞, ∞[ [-1, ∞[
![Page 14: World 2-1 Functions, Relations, Domain and Range.](https://reader035.fdocuments.in/reader035/viewer/2022062315/5697c0081a28abf838cc6e1a/html5/thumbnails/14.jpg)
4. Find the Domain and Range
D: ___________ R: ___________[-1, ∞[ ] -∞, ∞[
![Page 15: World 2-1 Functions, Relations, Domain and Range.](https://reader035.fdocuments.in/reader035/viewer/2022062315/5697c0081a28abf838cc6e1a/html5/thumbnails/15.jpg)
5. Find the Domain and Range
D: ___________ R: ___________]-6, 6[ ] -5, 5[
![Page 16: World 2-1 Functions, Relations, Domain and Range.](https://reader035.fdocuments.in/reader035/viewer/2022062315/5697c0081a28abf838cc6e1a/html5/thumbnails/16.jpg)
6. Find the Domain and Range
D: _______________ R: ___________[-∞, 0[ U ]0, ∞[ ] 0, ∞[
![Page 17: World 2-1 Functions, Relations, Domain and Range.](https://reader035.fdocuments.in/reader035/viewer/2022062315/5697c0081a28abf838cc6e1a/html5/thumbnails/17.jpg)
7. Find the Domain and Range
D: ___________ R: ___________{1,3,5} {4,5,6}
![Page 18: World 2-1 Functions, Relations, Domain and Range.](https://reader035.fdocuments.in/reader035/viewer/2022062315/5697c0081a28abf838cc6e1a/html5/thumbnails/18.jpg)
Homework
World 2-1 Homework