Section 1-4Graphs of Functions

Warm-upGive the domain and range of each function.

1. 1,29( ) , 2,41( ) , 3,12( ) , 4 ,81( ){ } 2. y = 4

3. y = x 4. y =

32x − 4

Warm-upGive the domain and range of each function.

1. 1,29( ) , 2,41( ) , 3,12( ) , 4 ,81( ){ } 2. y = 4

3. y = x 4. y =

32x − 4

D = {1, 2, 3, 4}

Warm-upGive the domain and range of each function.

1. 1,29( ) , 2,41( ) , 3,12( ) , 4 ,81( ){ } 2. y = 4

3. y = x 4. y =

32x − 4

D = {1, 2, 3, 4}R = {12, 29, 41, 81}

Warm-upGive the domain and range of each function.

1. 1,29( ) , 2,41( ) , 3,12( ) , 4 ,81( ){ } 2. y = 4

3. y = x 4. y =

32x − 4

D = {1, 2, 3, 4}R = {12, 29, 41, 81}

D = All real numbers

Warm-upGive the domain and range of each function.

1. 1,29( ) , 2,41( ) , 3,12( ) , 4 ,81( ){ } 2. y = 4

3. y = x 4. y =

32x − 4

D = {1, 2, 3, 4}R = {12, 29, 41, 81}

D = All real numbersR = {4}

Warm-upGive the domain and range of each function.

1. 1,29( ) , 2,41( ) , 3,12( ) , 4 ,81( ){ } 2. y = 4

3. y = x 4. y =

32x − 4

D = {1, 2, 3, 4}R = {12, 29, 41, 81}

D = All real numbersR = {4}

D = All real numbers

Warm-upGive the domain and range of each function.

1. 1,29( ) , 2,41( ) , 3,12( ) , 4 ,81( ){ } 2. y = 4

3. y = x 4. y =

32x − 4

D = {1, 2, 3, 4}R = {12, 29, 41, 81}

D = All real numbersR = {4}

D = All real numbersR = All non-negative numbers

Warm-upGive the domain and range of each function.

1. 1,29( ) , 2,41( ) , 3,12( ) , 4 ,81( ){ } 2. y = 4

3. y = x 4. y =

32x − 4

D = {1, 2, 3, 4}R = {12, 29, 41, 81}

D = All real numbersR = {4}

D = All real numbersR = All non-negative numbers

D = {x : x ≠ 2}

Warm-upGive the domain and range of each function.

1. 1,29( ) , 2,41( ) , 3,12( ) , 4 ,81( ){ } 2. y = 4

3. y = x 4. y =

32x − 4

D = {1, 2, 3, 4}R = {12, 29, 41, 81}

D = All real numbersR = {4}

D = All real numbersR = All non-negative numbers

D = {x : x ≠ 2} R = {y : y ≠ 0}

Horizontal Axis:

Horizontal Axis: Contains the independent variables

Horizontal Axis: Contains the independent variables

Vertical Axis:

Horizontal Axis: Contains the independent variables

Vertical Axis: Contains the dependent variables

Horizontal Axis: Contains the independent variables

Vertical Axis: Contains the dependent variables

Relation:

Horizontal Axis: Contains the independent variables

Vertical Axis: Contains the dependent variables

Relation: Any set of ordered pairs

Horizontal Axis: Contains the independent variables

Vertical Axis: Contains the dependent variables

Relation: Any set of ordered pairs

Any relationship between two variables can be written as a set of ordered pairs

Horizontal Axis: Contains the independent variables

Vertical Axis: Contains the dependent variables

Relation: Any set of ordered pairs

Any relationship between two variables can be written as a set of ordered pairs

Every function is a relation, but not ever relation is a function

Horizontal Axis: Contains the independent variables

Vertical Axis: Contains the dependent variables

Relation: Any set of ordered pairs

Any relationship between two variables can be written as a set of ordered pairs

Every function is a relation, but not ever relation is a function

A function is a relation where each first coordinate appears only once in all ordered pairs

Example 1Is the following a graph of a function?

6

4

2

-2

- 4

- 6

-10 - 5 5 10

Example 1Is the following a graph of a function?

6

4

2

-2

- 4

- 6

-10 - 5 5 10

No, there are many possible outcomes when you input a value of 3

Vertical-Line Test

Vertical-Line Test

If a vertical line can be drawn ANYWHERE on a graph and only touch the graph once, it is a function. If the vertical line

touches more than once, it is not a function.

Example 2Consider the line that is parallel to the x-axis and goes through the point (1, 4). Would this be a graph of a function? Justify

your answer.

Example 2Consider the line that is parallel to the x-axis and goes through the point (1, 4). Would this be a graph of a function? Justify

your answer.

This line is horizontal, so it passes the Vertical-Line Test. Thus, it is a function.

Example 3Make two sketches, where the first is a function and the

second is not (other than a vertical line).

Example 3Make two sketches, where the first is a function and the

second is not (other than a vertical line).

6

4

2

-2

- 4

- 6

-10 - 5 5 10

Example 3Make two sketches, where the first is a function and the

second is not (other than a vertical line).

6

4

2

-2

- 4

- 6

-10 - 5 5 10

6

4

2

-2

- 4

- 6

-10 - 5 5 10

Example 4State whether the following are functions or not.

6

4

2

-2

- 4

- 6

-10 - 5 5 10

a. 6

4

2

-2

- 4

- 6

-10 - 5 5 10

b.

Example 4State whether the following are functions or not.

6

4

2

-2

- 4

- 6

-10 - 5 5 10

a. 6

4

2

-2

- 4

- 6

-10 - 5 5 10

b.

Example 4State whether the following are functions or not.

6

4

2

-2

- 4

- 6

-10 - 5 5 10

a. 6

4

2

-2

- 4

- 6

-10 - 5 5 10

b.

Not a function;Fails Vertical-Line

Test

Example 4State whether the following are functions or not.

6

4

2

-2

- 4

- 6

-10 - 5 5 10

a. 6

4

2

-2

- 4

- 6

-10 - 5 5 10

b.

Not a function;Fails Vertical-Line

Test

Example 4State whether the following are functions or not.

6

4

2

-2

- 4

- 6

-10 - 5 5 10

a. 6

4

2

-2

- 4

- 6

-10 - 5 5 10

b.

Not a function;Fails Vertical-Line

Test

Is a function;Passes Vertical-Line

Test

Homework

Homework

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