Which Of The Following Relationships Is NOT A Function?1. \[$\{(8, -2), (6, -4), (4, -6), (2, -8), (0, -10)\}\$\]2. $\[ \begin{array}{c|c} x & Y \\ \hline 0 & 6 \\ 3 & 5 \\ 4 & 3 \\ -2 & 1 \\ \end{array} \\]3. Employee To Position: -

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Introduction

In mathematics, a function is a relation between a set of inputs, called the domain, and a set of possible outputs, called the range. It is a way of describing a relationship between two sets of values, where each input value corresponds to exactly one output value. In this article, we will explore three different relationships and determine which one is not a function.

Relationship 1: A Set of Ordered Pairs

The first relationship is given as a set of ordered pairs: {(8,−2),(6,−4),(4,−6),(2,−8),(0,−10)}\{(8, -2), (6, -4), (4, -6), (2, -8), (0, -10)\}. This set represents a relation between two sets of values, where each ordered pair consists of an input value and an output value.

**Relationship 1: A Set of Ordered Pairs**
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*   The input values are: 8, 6, 4, 2, 0
*   The output values are: -2, -4, -6, -8, -10

In this relationship, each input value corresponds to exactly one output value. For example, the input value 8 corresponds to the output value -2, and the input value 6 corresponds to the output value -4. This relationship is a function because each input value has a unique output value.

Relationship 2: A Table of Values

The second relationship is given as a table of values:

x y
0 6
3 5
4 3
-2 1

This table represents a relation between two sets of values, where each row consists of an input value and an output value.

**Relationship 2: A Table of Values**
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| Input Value (x) | Output Value (y) |
| --- | --- |
| 0 | 6 |
| 3 | 5 |
| 4 | 3 |
| -2 | 1 |

In this relationship, each input value corresponds to exactly one output value. For example, the input value 0 corresponds to the output value 6, and the input value 3 corresponds to the output value 5. This relationship is a function because each input value has a unique output value.

Relationship 3: A Many-to-One Relationship

The third relationship is given as a relation between employees and their positions:

Employee Position
John Manager
Jane Manager
Bob Salesperson
Alice Salesperson

This relationship represents a many-to-one relationship, where multiple employees can have the same position.

**Relationship 3: A Many-to-One Relationship**
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| Employee | Position |
| --- | --- |
| John | Manager |
| Jane | Manager |
| Bob | Salesperson |
| Alice | Salesperson |

In this relationship, the input values (employees) do not correspond to unique output values (positions). For example, both John and Jane have the same position, Manager. This relationship is not a function because each input value does not have a unique output value.

Conclusion

In conclusion, the relationship that is not a function is the third relationship, which is a many-to-one relationship between employees and their positions. This relationship is not a function because each input value (employee) does not correspond to a unique output value (position).

Key Takeaways

  • A function is a relation between a set of inputs and a set of possible outputs, where each input value corresponds to exactly one output value.
  • A relationship is not a function if each input value does not correspond to a unique output value.
  • A many-to-one relationship is not a function because each input value does not correspond to a unique output value.

References

Further Reading

Introduction

In our previous article, we explored three different relationships and determined which one is not a function. In this article, we will answer some frequently asked questions about functions and relationships.

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. It is a way of describing a relationship between two sets of values, where each input value corresponds to exactly one output value.

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

A: A relation is a set of ordered pairs, where each pair consists of an input value and an output value. A function is a relation where each input value corresponds to exactly one output value.

Q: Can a function have multiple output values?

A: No, a function cannot have multiple output values. Each input value must correspond to exactly one output value.

Q: Can a relation have multiple input values?

A: Yes, a relation can have multiple input values. However, if a relation has multiple input values that correspond to the same output value, it is not a function.

Q: What is a many-to-one relationship?

A: A many-to-one relationship is a relation where multiple input values correspond to the same output value.

Q: Is a many-to-one relationship a function?

A: No, a many-to-one relationship is not a function. Each input value must correspond to exactly one output value, and a many-to-one relationship does not meet this criteria.

Q: Can a function be represented as a table of values?

A: Yes, a function can be represented as a table of values. Each row in the table represents an input value and its corresponding output value.

Q: Can a function be represented as a set of ordered pairs?

A: Yes, a function can be represented as a set of ordered pairs. Each pair in the set represents an input value and its corresponding output value.

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

A: To determine if a relationship is a function, check if each input value corresponds to exactly one output value. If each input value has a unique output value, then the relationship is a function.

Q: What are some examples of functions in real life?

A: Some examples of functions in real life include:

  • A person's height as a function of their age
  • A car's speed as a function of the amount of gas in the tank
  • A company's profits as a function of the number of employees

Conclusion

In conclusion, functions and relationships are important concepts in mathematics. By understanding the difference between a function and a relation, and by being able to determine if a relationship is a function, you can better understand and work with functions in a variety of contexts.

Key Takeaways

  • A function is a relation between a set of inputs and a set of possible outputs, where each input value corresponds to exactly one output value.
  • A relation is a set of ordered pairs, where each pair consists of an input value and an output value.
  • A many-to-one relationship is not a function because each input value does not correspond to a unique output value.

References

Further Reading