![Page 1: Introduction to Functions Objective: State the domain and range of a relation and tell whether it is a function](https://reader034.vdocuments.net/reader034/viewer/2022051400/5513fad4550346dd488b45fe/html5/thumbnails/1.jpg)
Introduction to Functions
Objective: State the domain and range of a relation and tell whether it
is a function.
![Page 2: Introduction to Functions Objective: State the domain and range of a relation and tell whether it is a function](https://reader034.vdocuments.net/reader034/viewer/2022051400/5513fad4550346dd488b45fe/html5/thumbnails/2.jpg)
![Page 3: Introduction to Functions Objective: State the domain and range of a relation and tell whether it is a function](https://reader034.vdocuments.net/reader034/viewer/2022051400/5513fad4550346dd488b45fe/html5/thumbnails/3.jpg)
725 3)5.1(2 16)4( 2
44.1)2.1( 2 8)2( 3 001.0)1.0( 3
![Page 4: Introduction to Functions Objective: State the domain and range of a relation and tell whether it is a function](https://reader034.vdocuments.net/reader034/viewer/2022051400/5513fad4550346dd488b45fe/html5/thumbnails/4.jpg)
Functions
• A function is a relationship between two variables such that each value of the first variable is paired with exactly one value of the second variable.
![Page 5: Introduction to Functions Objective: State the domain and range of a relation and tell whether it is a function](https://reader034.vdocuments.net/reader034/viewer/2022051400/5513fad4550346dd488b45fe/html5/thumbnails/5.jpg)
Functions
• A function is a relationship between two variables such that each value of the first variable is paired with exactly one value of the second variable.
• The first variable (usually x) is called the domain of the function.
• The second variable (usually y) is called the range of the function.
![Page 6: Introduction to Functions Objective: State the domain and range of a relation and tell whether it is a function](https://reader034.vdocuments.net/reader034/viewer/2022051400/5513fad4550346dd488b45fe/html5/thumbnails/6.jpg)
Functions
• A function is a relationship between two variables such that each value of the first variable is paired with exactly one value of the second variable.
• The first variable (usually x) is called the domain of the function.
• The second variable (usually y) is called the range of the function.
• For every value of x, there is one and only one value for y.
![Page 7: Introduction to Functions Objective: State the domain and range of a relation and tell whether it is a function](https://reader034.vdocuments.net/reader034/viewer/2022051400/5513fad4550346dd488b45fe/html5/thumbnails/7.jpg)
Example 1
![Page 8: Introduction to Functions Objective: State the domain and range of a relation and tell whether it is a function](https://reader034.vdocuments.net/reader034/viewer/2022051400/5513fad4550346dd488b45fe/html5/thumbnails/8.jpg)
Example 1
![Page 9: Introduction to Functions Objective: State the domain and range of a relation and tell whether it is a function](https://reader034.vdocuments.net/reader034/viewer/2022051400/5513fad4550346dd488b45fe/html5/thumbnails/9.jpg)
Example 1
![Page 10: Introduction to Functions Objective: State the domain and range of a relation and tell whether it is a function](https://reader034.vdocuments.net/reader034/viewer/2022051400/5513fad4550346dd488b45fe/html5/thumbnails/10.jpg)
Try This
• State whether the data in each table represents a function.
![Page 11: Introduction to Functions Objective: State the domain and range of a relation and tell whether it is a function](https://reader034.vdocuments.net/reader034/viewer/2022051400/5513fad4550346dd488b45fe/html5/thumbnails/11.jpg)
Try This
• State whether the data in each table represents a function.
yes
![Page 12: Introduction to Functions Objective: State the domain and range of a relation and tell whether it is a function](https://reader034.vdocuments.net/reader034/viewer/2022051400/5513fad4550346dd488b45fe/html5/thumbnails/12.jpg)
Try This
• State whether the data in each table represents a function.
yes yes
![Page 13: Introduction to Functions Objective: State the domain and range of a relation and tell whether it is a function](https://reader034.vdocuments.net/reader034/viewer/2022051400/5513fad4550346dd488b45fe/html5/thumbnails/13.jpg)
Try This
• State whether the data in each table represents a function.
yes yes no
![Page 14: Introduction to Functions Objective: State the domain and range of a relation and tell whether it is a function](https://reader034.vdocuments.net/reader034/viewer/2022051400/5513fad4550346dd488b45fe/html5/thumbnails/14.jpg)
Vertical Line Test
• Remember that a vertical line is a line with the equation x = c, where c is an arbitrary constant. All points on the line have the same x-coordinate. If a vertical line crosses a graph more than once, that means for that one value of x there will be more than one value for y.
![Page 15: Introduction to Functions Objective: State the domain and range of a relation and tell whether it is a function](https://reader034.vdocuments.net/reader034/viewer/2022051400/5513fad4550346dd488b45fe/html5/thumbnails/15.jpg)
Vertical Line Test
• Remember that a vertical line is a line with the equation x = c, where c is an arbitrary constant. All points on the line have the same x-coordinate. If a vertical line crosses a graph more than once, that means for that one value of x there will be more than one value for y.
• If every vertical line intersects a graph at no more than one point, then the graph represents a function.
![Page 16: Introduction to Functions Objective: State the domain and range of a relation and tell whether it is a function](https://reader034.vdocuments.net/reader034/viewer/2022051400/5513fad4550346dd488b45fe/html5/thumbnails/16.jpg)
Example 2
![Page 17: Introduction to Functions Objective: State the domain and range of a relation and tell whether it is a function](https://reader034.vdocuments.net/reader034/viewer/2022051400/5513fad4550346dd488b45fe/html5/thumbnails/17.jpg)
Definition of a Relation
• A relationship between two variables such that each value of the first variable is paired with one or more values of the second variable is called a relation.
• The domain is the set of all possible values of the first variable. The range is the set of all possible values of the second variable.
![Page 18: Introduction to Functions Objective: State the domain and range of a relation and tell whether it is a function](https://reader034.vdocuments.net/reader034/viewer/2022051400/5513fad4550346dd488b45fe/html5/thumbnails/18.jpg)
Example 4
![Page 19: Introduction to Functions Objective: State the domain and range of a relation and tell whether it is a function](https://reader034.vdocuments.net/reader034/viewer/2022051400/5513fad4550346dd488b45fe/html5/thumbnails/19.jpg)
Example 4
![Page 20: Introduction to Functions Objective: State the domain and range of a relation and tell whether it is a function](https://reader034.vdocuments.net/reader034/viewer/2022051400/5513fad4550346dd488b45fe/html5/thumbnails/20.jpg)
Try This
![Page 21: Introduction to Functions Objective: State the domain and range of a relation and tell whether it is a function](https://reader034.vdocuments.net/reader034/viewer/2022051400/5513fad4550346dd488b45fe/html5/thumbnails/21.jpg)
Try This
}2,1,0,3{ range
}5,3,2,1,3,4{domain
1 range
2domain
y
x
![Page 22: Introduction to Functions Objective: State the domain and range of a relation and tell whether it is a function](https://reader034.vdocuments.net/reader034/viewer/2022051400/5513fad4550346dd488b45fe/html5/thumbnails/22.jpg)
Function Notation
![Page 23: Introduction to Functions Objective: State the domain and range of a relation and tell whether it is a function](https://reader034.vdocuments.net/reader034/viewer/2022051400/5513fad4550346dd488b45fe/html5/thumbnails/23.jpg)
Function Notation
![Page 24: Introduction to Functions Objective: State the domain and range of a relation and tell whether it is a function](https://reader034.vdocuments.net/reader034/viewer/2022051400/5513fad4550346dd488b45fe/html5/thumbnails/24.jpg)
Example 5
![Page 25: Introduction to Functions Objective: State the domain and range of a relation and tell whether it is a function](https://reader034.vdocuments.net/reader034/viewer/2022051400/5513fad4550346dd488b45fe/html5/thumbnails/25.jpg)
Example 5
![Page 26: Introduction to Functions Objective: State the domain and range of a relation and tell whether it is a function](https://reader034.vdocuments.net/reader034/viewer/2022051400/5513fad4550346dd488b45fe/html5/thumbnails/26.jpg)
Example 6
![Page 27: Introduction to Functions Objective: State the domain and range of a relation and tell whether it is a function](https://reader034.vdocuments.net/reader034/viewer/2022051400/5513fad4550346dd488b45fe/html5/thumbnails/27.jpg)
Example 6
![Page 28: Introduction to Functions Objective: State the domain and range of a relation and tell whether it is a function](https://reader034.vdocuments.net/reader034/viewer/2022051400/5513fad4550346dd488b45fe/html5/thumbnails/28.jpg)
![Page 29: Introduction to Functions Objective: State the domain and range of a relation and tell whether it is a function](https://reader034.vdocuments.net/reader034/viewer/2022051400/5513fad4550346dd488b45fe/html5/thumbnails/29.jpg)
Homework
• Pages 108-109• 17-49 odd