{ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline -6 & -7 \\ \hline -1 & 1 \\ \hline 0 & 9 \\ \hline 3 & -2 \\ \hline \end{tabular} \}$What Is The Domain Of The Given Function?A. $\{x \mid X=-6,-1,0,3\}$B. $\{y \mid

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Introduction

When dealing with functions, it's essential to understand the concept of domain and range. The domain of a function is the set of all possible input values (x-values) for which the function is defined, while the range is the set of all possible output values (y-values). In this article, we will explore the domain of a given function represented in a table.

Understanding the Table

The given table represents a function with input values (x) and corresponding output values (y). The table is as follows:

x y
-6 -7
-1 1
0 9
3 -2

Domain of a Function

The domain of a function is the set of all possible input values (x-values) for which the function is defined. In other words, it's the set of all x-values that can be plugged into the function to produce a valid output value (y-value).

Analyzing the Table

Looking at the table, we can see that there are four input values (x-values) corresponding to four output values (y-values). The input values are -6, -1, 0, and 3. Since there are no restrictions on the input values, we can conclude that the domain of the function is the set of all possible input values.

Domain Representation

The domain of the function can be represented as:

{x∣x=−6,−1,0,3}\{x \mid x=-6,-1,0,3\}

This notation indicates that the domain of the function consists of the four input values -6, -1, 0, and 3.

Conclusion

In conclusion, the domain of the given function is the set of all possible input values (x-values) for which the function is defined. Based on the table, we can conclude that the domain of the function is the set of all possible input values, which can be represented as:

{x∣x=−6,−1,0,3}\{x \mid x=-6,-1,0,3\}

This notation indicates that the domain of the function consists of the four input values -6, -1, 0, and 3.

Range of a Function

The range of a function is the set of all possible output values (y-values) for which the function is defined. In other words, it's the set of all y-values that can be produced by plugging in the input values (x-values).

Analyzing the Table

Looking at the table, we can see that there are four output values (y-values) corresponding to four input values (x-values). The output values are -7, 1, 9, and -2. Since there are no restrictions on the output values, we can conclude that the range of the function is the set of all possible output values.

Range Representation

The range of the function can be represented as:

{y∣y=−7,1,9,−2}\{y \mid y=-7,1,9,-2\}

This notation indicates that the range of the function consists of the four output values -7, 1, 9, and -2.

Conclusion

In conclusion, the range of the given function is the set of all possible output values (y-values) for which the function is defined. Based on the table, we can conclude that the range of the function is the set of all possible output values, which can be represented as:

{y∣y=−7,1,9,−2}\{y \mid y=-7,1,9,-2\}

This notation indicates that the range of the function consists of the four output values -7, 1, 9, and -2.

Domain and Range of a Function

In conclusion, the domain of the given function is the set of all possible input values (x-values) for which the function is defined, while the range is the set of all possible output values (y-values). The domain can be represented as:

{x∣x=−6,−1,0,3}\{x \mid x=-6,-1,0,3\}

The range can be represented as:

{y∣y=−7,1,9,−2}\{y \mid y=-7,1,9,-2\}

This notation indicates that the domain and range of the function consist of the four input values -6, -1, 0, and 3, and the four output values -7, 1, 9, and -2, respectively.

Final Conclusion

In conclusion, the domain and range of a function are essential concepts in mathematics that help us understand the behavior of a function. The domain represents the set of all possible input values (x-values) for which the function is defined, while the range represents the set of all possible output values (y-values). By analyzing the table, we can conclude that the domain of the given function is the set of all possible input values, which can be represented as:

{x∣x=−6,−1,0,3}\{x \mid x=-6,-1,0,3\}

The range of the function is the set of all possible output values, which can be represented as:

{y∣y=−7,1,9,−2}\{y \mid y=-7,1,9,-2\}

This notation indicates that the domain and range of the function consist of the four input values -6, -1, 0, and 3, and the four output values -7, 1, 9, and -2, respectively.

Introduction

In our previous article, we explored the concept of domain and range of a function, and how to determine them using a table. In this article, we will answer some frequently asked questions related to domain and range of a function.

Q: What is the domain of a function?

A: The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Q: How do I determine the domain of a function?

A: To determine the domain of a function, you need to look at the table and identify all the input values (x-values) that correspond to valid output values (y-values).

Q: What is the range of a function?

A: The range of a function is the set of all possible output values (y-values) for which the function is defined.

Q: How do I determine the range of a function?

A: To determine the range of a function, you need to look at the table and identify all the output values (y-values) that correspond to valid input values (x-values).

Q: Can the domain and range of a function be the same?

A: Yes, the domain and range of a function can be the same. This occurs when the function is a one-to-one function, meaning that each input value (x-value) corresponds to a unique output value (y-value).

Q: Can the domain of a function be empty?

A: Yes, the domain of a function can be empty. This occurs when there are no input values (x-values) that correspond to valid output values (y-values).

Q: Can the range of a function be empty?

A: Yes, the range of a function can be empty. This occurs when there are no output values (y-values) that correspond to valid input values (x-values).

Q: How do I represent the domain and range of a function?

A: The domain and range of a function can be represented using set notation. For example, the domain of a function can be represented as:

{x∣x=−6,−1,0,3}\{x \mid x=-6,-1,0,3\}

The range of a function can be represented as:

{y∣y=−7,1,9,−2}\{y \mid y=-7,1,9,-2\}

Q: What is the difference between the domain and range of a function?

A: The domain of a function is the set of all possible input values (x-values) for which the function is defined, while the range is the set of all possible output values (y-values). In other words, the domain represents the input values, while the range represents the output values.

Q: Can the domain and range of a function be infinite?

A: Yes, the domain and range of a function can be infinite. This occurs when the function is defined for all real numbers, or when the function produces all real numbers as output values.

Q: Can the domain and range of a function be a combination of numbers and variables?

A: Yes, the domain and range of a function can be a combination of numbers and variables. This occurs when the function is defined using algebraic expressions that involve variables.

Conclusion

In conclusion, the domain and range of a function are essential concepts in mathematics that help us understand the behavior of a function. By answering these frequently asked questions, we hope to have provided a better understanding of the domain and range of a function.

Final Tips

  • Always remember that the domain of a function is the set of all possible input values (x-values) for which the function is defined.
  • Always remember that the range of a function is the set of all possible output values (y-values) for which the function is defined.
  • Use set notation to represent the domain and range of a function.
  • Be careful when determining the domain and range of a function, as it can be easy to make mistakes.

References

  • [1] "Domain and Range of a Function" by Math Open Reference
  • [2] "Domain and Range" by Khan Academy
  • [3] "Domain and Range of a Function" by Wolfram MathWorld

Glossary

  • Domain: The set of all possible input values (x-values) for which the function is defined.
  • Range: The set of all possible output values (y-values) for which the function is defined.
  • Set notation: A way of representing a set of values using curly brackets and a colon.
  • One-to-one function: A function that maps each input value (x-value) to a unique output value (y-value).
  • Empty set: A set that contains no elements.
  • Infinite set: A set that contains an infinite number of elements.