Functions and Relations: Domain and Range

Questions and Answers

What is the domain of the relation {(2, 3), (4, 5), (6, 7)}?

{5, 6, 7}

{2, 4, 6} (correct)

{2, 3, 4}

{3, 5, 7}

If a relation has the ordered pairs {(1, -1), (1, 2), (3, 4)}, what can be concluded about it?

It has a range of {-1, 2, 4}.

It has a domain of {1, 3}.

It is not a function due to non-unique outputs. (correct)

It is a function since the inputs are the same.

For the relation {(0, 1), (1, 0), (2, 1)}, what is the range?

{0, 1} (correct)

{0, 1, 2, 3}

{0, 1, 2}

{1}

Which of the following correctly identifies restrictions that might affect the domain of a function?

Having inputs that result in division by zero. Signup and view all the answers

What would be the implication if a vertical line intersects the graph of a relation at more than one point?

The relation is not a function. Signup and view all the answers

Given the relation {(2, 3), (3, 5), (5, 3)}, what is the domain and range?

Domain: {2, 3, 5}, Range: {3, 5} Signup and view all the answers

Study Notes

Relations

A relation is a set of ordered pairs (x, y).
Each ordered pair consists of an input (x) and an output (y).

Functions

A function is a special type of relation where each input (x) corresponds to exactly one output (y).
Notation: f(x) denotes the function value for input x.

Domain

The domain of a relation or function is the complete set of possible input values (x-values).
To find the domain:
- Identify all potential x-values from the set of ordered pairs.
- Consider restrictions (e.g., division by zero, square roots of negative numbers).

Range

The range of a relation or function is the complete set of possible output values (y-values).
To find the range:
- Identify all potential y-values from the set of ordered pairs.
- Look for any restrictions on output values.

Key Concepts

Example of Domain and Range:
- For the relation {(1, 2), (3, 4), (5, 6)}, the domain is {1, 3, 5} and the range is {2, 4, 6}.
Vertical Line Test:
- A visual method to determine if a relation is a function. If a vertical line intersects the graph of the relation at more than one point, it is not a function.

Relations

A relation consists of ordered pairs (x, y), associating inputs (x) with outputs (y).

Functions

A function is a specific type of relation where each input (x) links to one and only one output (y).
Function notation is represented as f(x), indicating the function's output value for a given input x.

Domain

The domain refers to the complete set of all possible input values (x-values) for a relation or function.
To determine the domain:
- Identify all x-values from the ordered pairs.
- Take into account any restrictions, such as avoiding division by zero or square roots of negative numbers.

Range

The range represents the complete set of possible output values (y-values) for a relation or function.
To determine the range:
- Identify all y-values from the ordered pairs.
- Consider any restrictions affecting output values.

Key Concepts

Example of Domain and Range:
- For the relation {(1, 2), (3, 4), (5, 6)}, the identified domain is {1, 3, 5} and the range is {2, 4, 6}.
Vertical Line Test:
- A technique for determining if a relation qualifies as a function.
- If a vertical line intersects a graph of the relation at more than one point, it indicates that the relation is not a function.

Description

This quiz explores the concepts of relations and functions, focusing on the definitions of domain and range. Participants will learn how to identify the domain and range from sets of ordered pairs and understand the importance of these concepts in mathematics.