Examine the following tables of ordered pairs and identify which relations are functions

Oct 13, 2025 by windailys.com 45 views

Examine the following tables of ordered pairs and identify which relations are functions

In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). A function is a special type of relation where each input is associated with exactly one output. In this article, we will examine several tables of ordered pairs and determine which relations are functions.

$x$	$y$
0	4
1	5
2	6
1	7
0	8

Is Table 1 a function?

To determine if Table 1 is a function, we need to check if each input is associated with exactly one output. Looking at the table, we see that the input $x=1$ is associated with two different outputs: $y=5$ and $y=7$ . This means that Table 1 is not a function.

Why is Table 1 not a function?

A function must have the property that each input is associated with exactly one output. In Table 1, the input $x=1$ is associated with two different outputs: $y=5$ and $y=7$ . This means that Table 1 does not satisfy the definition of a function.

$x$	$y$
0	4
1	5
2	6
3	7
4	8

Is Table 2 a function?

To determine if Table 2 is a function, we need to check if each input is associated with exactly one output. Looking at the table, we see that each input is associated with exactly one output. For example, the input $x=0$ is associated with the output $y=4$ , and the input $x=1$ is associated with the output $y=5$ . This means that Table 2 is a function.

Why is Table 2 a function?

A function must have the property that each input is associated with exactly one output. In Table 2, each input is associated with exactly one output. For example, the input $x=0$ is associated with the output $y=4$ , and the input $x=1$ is associated with the output $y=5$ . This means that Table 2 satisfies the definition of a function.

$x$	$y$
0	4
1	5
2	6
3	7
4	8
$x$	$y$
---	---
5	9
6	10
7	11
8	12

Is Table 3 a function?

To determine if Table 3 is a function, we need to check if each input is associated with exactly one output. Looking at the table, we see that each input is associated with exactly one output. For example, the input $x=0$ is associated with the output $y=4$ , and the input $x=1$ is associated with the output $y=5$ . This means that Table 3 is a function.

Why is Table 3 a function?

A function must have the property that each input is associated with exactly one output. In Table 3, each input is associated with exactly one output. For example, the input $x=0$ is associated with the output $y=4$ , and the input $x=1$ is associated with the output $y=5$ . This means that Table 3 satisfies the definition of a function.

In conclusion, we have examined three tables of ordered pairs and determined which relations are functions. Table 1 is not a function because each input is associated with more than one output. Table 2 is a function because each input is associated with exactly one output. Table 3 is also a function because each input is associated with exactly one output.

A function must have the property that each input is associated with exactly one output.
A relation is not a function if each input is associated with more than one output.
A relation is a function if each input is associated with exactly one output.

Q: What is a function?

A: A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range). A function is a special type of relation where each input is associated with exactly one output.

Q: What is a relation?

A: A relation is a set of ordered pairs that satisfy certain conditions. In other words, a relation is a way of describing the relationship between two sets of values.

Q: What is the difference between a function and a relation?

A: The main difference between a function and a relation is that a function must have the property that each input is associated with exactly one output. A relation, on the other hand, can have multiple outputs for a single input.

Q: How do I determine if a relation is a function?

A: To determine if a relation is a function, you need to check if each input is associated with exactly one output. If each input is associated with more than one output, then the relation is not a function.

Q: What are some examples of functions?

A: Some examples of functions include:

The function f(x) = 2x, which takes an input x and returns an output that is twice the value of x.
The function g(x) = x^2, which takes an input x and returns an output that is the square of x.
The function h(x) = 3x + 2, which takes an input x and returns an output that is three times the value of x plus 2.

Q: What are some examples of relations that are not functions?

A: Some examples of relations that are not functions include:

The relation {(1, 2), (1, 3), (2, 4)}, which has multiple outputs for a single input.
The relation {(x, y) | x = 1 and y = 2 or 3}, which has multiple outputs for a single input.
The relation {(x, y) | x = 2 and y = 4 or 5}, which has multiple outputs for a single input.

Q: Can a relation be both a function and a relation?

A: Yes, a relation can be both a function and a relation. In fact, all functions are relations, but not all relations are functions.

Q: What is the importance of functions in mathematics?

A: Functions are important in mathematics because they provide a way of describing the relationship between two sets of values. Functions are used in many areas of mathematics, including algebra, geometry, and calculus.

Q: How do I use functions in real-life situations?

A: Functions are used in many real-life situations, including:

Modeling population growth
Describing the motion of objects
Calculating the area and perimeter of shapes
Determining the cost of goods and services

Q: What are some common mistakes to avoid when working with functions?

A: Some common mistakes to avoid when working with functions include:

Assuming that a relation is a function when it is not.
Failing to check if each input is associated with exactly one output.
Not using the correct notation when writing functions.

Q: How do I practice working with functions?

A: To practice working with functions, try the following:

Work through examples of functions and relations.
Practice writing functions in different notations.
Use functions to solve real-life problems.
Take online courses or watch video tutorials to learn more about functions.