Type The Correct Answer In The Box.$\[ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 3 & 10 \\ \hline $\square$ & 20 \\ \hline \end{tabular} \\]In The Table, The Relation $(x, Y)$ Is Not A Function If The Missing Value Of

What is a Function in Mathematics?

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 other words, a function is a rule that assigns to each input value a unique output value.

Key Characteristics of a Function

A function must satisfy the following key characteristics:

• Each input value corresponds to exactly one output value: This means that for every input value, there is only one possible output value.
• The output value is determined by the input value: This means that the output value is a function of the input value, and not a random value.

What is a Relation in Mathematics?

A relation is a set of ordered pairs that satisfy a certain condition. It is a way of describing a relationship between two sets of values, where each input value corresponds to one or more output values.

Key Characteristics of a Relation

A relation must satisfy the following key characteristics:

• Each input value corresponds to one or more output values: This means that for every input value, there is at least one possible output value.
• The output value is not necessarily determined by the input value: This means that the output value is not a function of the input value.

Is the Given Relation a Function?

The given relation is represented in a table as follows:

$x$	$y$
3	10
$\square$	20

To determine if the given relation is a function, we need to check if each input value corresponds to exactly one output value.

Analyzing the Given Relation

From the table, we can see that the input value 3 corresponds to the output value 10. However, the input value $\square$ corresponds to the output value 20.

Conclusion

Since the input value $\square$ corresponds to the output value 20, and there is no indication that the output value is determined by the input value, we can conclude that the given relation is not a function.

Why is the Given Relation Not a Function?

The given relation is not a function because the input value $\square$ corresponds to the output value 20, and there is no indication that the output value is determined by the input value. In other words, the output value is not a function of the input value.

What is the Missing Value in the Table?

The missing value in the table is the input value $\square$. To determine the missing value, we need to analyze the given relation and find the input value that corresponds to the output value 20.

Finding the Missing Value

From the table, we can see that the output value 20 corresponds to the input value $\square$. However, we also know that the input value 3 corresponds to the output value 10. Since the output value 20 is not equal to the output value 10, we can conclude that the input value $\square$ is not equal to the input value 3.

Conclusion

The missing value in the table is the input value 5.

Why is the Input Value 5 the Correct Answer?

The input value 5 is the correct answer because it is the only input value that corresponds to the output value 20. In other words, the input value 5 is the only input value that satisfies the given relation.

Final Answer

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Q: What is a function in mathematics?

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 are the key characteristics of a function?

A: A function must satisfy the following key characteristics:

• Each input value corresponds to exactly one output value: This means that for every input value, there is only one possible output value.
• The output value is determined by the input value: This means that the output value is a function of the input value, and not a random value.

Q: What is a relation in mathematics?

A: A relation is a set of ordered pairs that satisfy a certain condition. It is a way of describing a relationship between two sets of values, where each input value corresponds to one or more output values.

Q: What are the key characteristics of a relation?

A: A relation must satisfy the following key characteristics:

• Each input value corresponds to one or more output values: This means that for every input value, there is at least one possible output value.
• The output value is not necessarily determined by the input value: This means that the output value is not a function of the input value.

Q: Is the given relation a function?

A: No, the given relation is not a function. This is because the input value $\square$ corresponds to the output value 20, and there is no indication that the output value is determined by the input value.

Q: Why is the given relation not a function?

A: The given relation is not a function because the input value $\square$ corresponds to the output value 20, and there is no indication that the output value is determined by the input value. In other words, the output value is not a function of the input value.

Q: What is the missing value in the table?

A: The missing value in the table is the input value $\square$. To determine the missing value, we need to analyze the given relation and find the input value that corresponds to the output value 20.

Q: How do I find the missing value?

A: To find the missing value, we need to analyze the given relation and find the input value that corresponds to the output value 20. In this case, the input value 5 corresponds to the output value 20.

Q: Why is the input value 5 the correct answer?

A: The input value 5 is the correct answer because it is the only input value that corresponds to the output value 20. In other words, the input value 5 is the only input value that satisfies the given relation.

Q: What is the final answer?

A: The final answer is $\boxed{5}$.

Common Mistakes to Avoid

• Assuming a relation is a function without checking the key characteristics: Make sure to check if each input value corresponds to exactly one output value and if the output value is determined by the input value.
• Not analyzing the given relation carefully: Take your time to analyze the given relation and find the input value that corresponds to the output value.
• Not checking for multiple output values: Make sure to check if there are multiple output values for a given input value.

Conclusion

Understanding functions and relations in mathematics is crucial for solving problems and making informed decisions. By following the key characteristics of a function and a relation, you can determine if a given relation is a function or not. Remember to analyze the given relation carefully and check for multiple output values to avoid common mistakes.