math 71 2.2 – graphs of functions 1. graph of a function: the graph of all the function’s...

1

Math 71

2.2 – Graphs of Functions

2

Graph of a function:the graph of all the function’s ordered pairs

3

To test if a graph is a function we can use the __________________________________.

If any vertical line intersects a graph in two or more points, then the graph does not represent a function.

4

To test if a graph is a function we can use the __________________________________.

If any vertical line intersects a graph in two or more points, then the graph does not represent a function.

vertical line test

5

Ex 1.Which of the following graphs are functions?

6

Ex 1.Which of the following graphs are functions?

7

domain – set of all possible _________ ______range – set of all possible _________________

Domain and Range of Functions

8

domain – set of all possible _________ ______range – set of all possible _________________

Domain and Range of Functions

-values

9

domain – set of all possible _________ ______range – set of all possible _________________

Domain and Range of Functions

-values-values

10

Ex 2.Use the graph of each function to find its domain and range.

Domain __________________________ Domain __________________________

Range __________________________ Range __________________________

Domain and Range of Functions

11

Ex 2.Use the graph of each function to find its domain and range.

Domain __________________________ Domain __________________________

Range __________________________ Range __________________________

Domain and Range of Functions

{𝒙|−𝟐<𝒙≤𝟒 }

12

Ex 2.Use the graph of each function to find its domain and range.

Domain __________________________ Domain __________________________

Range __________________________ Range __________________________

Domain and Range of Functions

{𝒙|−𝟐<𝒙≤𝟒 }

{𝒚|−𝟐<𝒚 ≤𝟏 }

13

Ex 2.Use the graph of each function to find its domain and range.

Domain __________________________ Domain __________________________

Range __________________________ Range __________________________

Domain and Range of Functions

{𝒙|−𝟐<𝒙≤𝟒 }

{𝒚|−𝟐<𝒚 ≤𝟏 }

{𝒙|−𝟑≤ 𝒙<𝟒 }

14

Ex 2.Use the graph of each function to find its domain and range.

Domain __________________________ Domain __________________________

Range __________________________ Range __________________________

Domain and Range of Functions

{𝒙|−𝟐<𝒙≤𝟒 }

{𝒚|−𝟐<𝒚 ≤𝟏 }

{𝒙|−𝟑≤ 𝒙<𝟒 }

{𝒚|−𝟏≤𝒚 ≤𝟐 }

15

Ex 2.Use the graph of each function to find its domain and range.

Domain __________________________ Domain __________________________

Range __________________________ Range __________________________

Domain and Range of Functions

16

Ex 2.Use the graph of each function to find its domain and range.

Domain __________________________ Domain __________________________

Range __________________________ Range __________________________

Domain and Range of Functions

{𝒙|𝒙≥−𝟐 }

17

Ex 2.Use the graph of each function to find its domain and range.

Domain __________________________ Domain __________________________

Range __________________________ Range __________________________

Domain and Range of Functions

{𝒙|𝒙≥−𝟐 }

{𝒚|𝒚 ≥𝟏 }

18

Ex 2.Use the graph of each function to find its domain and range.

Domain __________________________ Domain __________________________

Range __________________________ Range __________________________

Domain and Range of Functions

{𝒙|𝒙≥−𝟐 }

{𝒚|𝒚 ≥𝟏 }

{𝒙|−𝟏≤ 𝒙≤𝟑 }

19

Ex 2.Use the graph of each function to find its domain and range.

Domain __________________________ Domain __________________________

Range __________________________ Range __________________________

Domain and Range of Functions

{𝒙|𝒙≥−𝟐 }

{𝒚|𝒚 ≥𝟏 }

{𝒙|−𝟏≤ 𝒙≤𝟑 }

{𝒚|𝟎≤ 𝒚 ≤𝟐 }

20

Ex 2.Use the graph of each function to find its domain and range.

Domain __________________________

Range __________________________

Domain and Range of Functions

21

Ex 2.Use the graph of each function to find its domain and range.

Domain __________________________

Range __________________________

Domain and Range of Functions

{𝒙|−𝟏≤ 𝒙<𝟑 }

22

Ex 2.Use the graph of each function to find its domain and range.

Domain __________________________

Range __________________________

Domain and Range of Functions

{𝒙|−𝟏≤ 𝒙<𝟑 }

{𝒚|𝒚=𝟐 ,𝟑 ,𝟒 }