Lesson 4.6- Relations & Functions

​Relations & Functions:

Objective:

• Identify the domain and range of a function.

• Use graphs, tables, and mapping diagrams to identify if a relation is a function.​

​Relations

• Another name for the relationship between independent and dependent variables, or a coordinate (x, y)

• Domain is the name for the x coordinate

• Range is the name for the y coordinate​

• Example: (-2, 3), (-1, 5), (3, 9), (4, 11)

• Domain is {-2, -1, 3, 4} Range is {3, 5, 9, 11}​

​How to find Domain & Range

​To identify domain and range from coordinates:

-First list the x values, then list the y values

To identify domain and range from a graph:

-Identify what the x values are, then the​ y values

Note: how to write as inequality​

Multiple Choice

All of the x values or inputs are called what?

• Domain

• Range

• Relation

• Function

Multiple Choice

All of the y values or outputs are called what?

• Domain

• Range

• Relation

• Function

Multiple Choice

DOMAIN is found by reading the ends of a graph from ___ to ___.

• Right to left

• Left to right

• Bottom to top

• Top to bottom

Multiple Choice

RANGE is found by reading the ends of a graph from ___ to ___.

• Right to left

• Left to right

• Bottom to top

• Top to bottom

Multiple Choice

For the function {(0,1), (1,-3), (2,-4), (-4,1)}, write the domain and range.

• D: {1, -3, -4,} R: {0, 1, 2, -4}

• D:{0, 1, 2, -4} R:{1, -3, -4}

• D:{0, 1, 2, 3, 4} R:{1, -3, -4}

Multiple Choice

• {1, 2, 3, 4, 5}

• {-1, 1, 2, 3}

• {1, 2, 3, 5}

• [1, 5]

Multiple Choice

What is the DOMAIN?

• {1, 2, 3, 4}

• {-3, 0, 3}

• {-3, 1, 2, 5}

• {1, 2, -3, 5}

Use coordinates, mapping diagram, or vertical line test.​

​

​Determining Functions:

​

Multiple Choice

• Function

• Not a Function

Multiple Choice

Is this mapping a function or not a function? 

• Function

• Not a Function

Multiple Choice

Is this graph a function or not a function? 

• Function

• Not a Function

Multiple Choice

What is the domain of the graph?

• {-4, 0, 2, 4}

• {-5, -4, -3, -1}

• {-5, -4, -3, -1, 0, 2, 4}

• All real numbers

Multiple Choice

Is this mapping a function or not a function? 

• Function

• Not a Function 

Multiple Choice

Is this graph a function or not a function? 

• Function

• Not a Function

Multiple Choice

Is this table a function or not a function? 

• Function

• Not a Function

Multiple Choice

Which set of values is a function?

• (9,5) (10,5) (9,-5) (10,-5)

• (3,4) (4,-3) (7,4) (3, 8)

• (6,-5) (7, -3) (8, -1) (9, 1)

• (2, -2) (5, 9) (5, -7) (1, 4)

Multiple Choice

Is the relation a function? Why.

• Yes, because the x-value 11 has two y-values pair with it.

• Yes, because each x-value has only one y-value paired with it.

• No, because the x-value 11 has two y-values pair with it.

• No, because each x-value has only one y-value paired with it.

Multiple Choice

In the given relation, what domain value corresponds to the range value -2?

{(-1, 2), (-2, 4), (2, 5), (0, -2), (2, 0)}

• -2

• 2

• 4

• 0

Multiple Choice

What is the range?

• {-2,2,5}

• {1,3,5,6}

• all real numbers 

• -2<y<5

Multiple Choice

The left grouping in a mapping is the

• Domain

• range

• relation

• y-axis

Multiple Choice

What is the RANGE of this graph?

• -7<x<5

• -7≤y<5

• -3<x<1

• -3≤y<1

Multiple Choice

What is the range?

• -4 < x ≤ 5

• -4 ≤ x < 5

• -3 < y < 3

• -3 ≤ y ≤ 3

Multiple Choice

What is the DOMAIN of this graph?

• -4 ≤ x ≤ 3

• -1 ≤ x ≤ 4

• 4 < x < 3

• -1 < x < 4

Multiple Choice

Which of the inequalities below best describes the domain of the function shown on the graph?

• -2 ≤ x ≤ 2

• -5 ≤ x ≤ -3

• -2 ≤ x ≤ 3

• -5 ≤ x ≤ 3

Multiple Choice

What is the Range?

• y ≥ 6

• $$y\le6$$  

• -10 ≤ y ≤ 6

• -10 ≤ x ≤ 6

Multiple Choice

What is the DOMAIN of this function?

• -∞ ≤ x ≤ ∞

• -∞ ≤ x ≤ ∞

• ∞ < x < ∞

• -∞ < x < ∞