What Are The Inputs Of The Function Below?${ \begin{tabular}{|c|c|c|c|c|} \hline X X X & -8 & 2 & 4 & 6 \ \hline F ( X ) F(x) F ( X ) & -6 & -3 & 1 & 5 \ \hline \end{tabular} }$A. { -6, -3, 1, 5$}$B. { -6, -3, 4, 6$} C . \[ C. \[ C . \[ -8, 2,

Mar 13, 2025 by ADMIN 245 views

What are the inputs of the function below?

Understanding the Function

The given function is represented in a table format, where the input values of $x$ are paired with their corresponding output values of $f(x)$ . To determine the inputs of the function, we need to identify the values of $x$ that are associated with the given output values of $f(x)$ .

Identifying the Inputs

Looking at the table, we can see that the output values of $f(x)$ are -6, -3, 1, and 5. To find the corresponding input values of $x$ , we need to match these output values with their respective input values in the table.

Matching Output Values with Input Values

The output value of $f(x)$ is -6, which corresponds to the input value of $x$ = -8.
The output value of $f(x)$ is -3, which corresponds to the input value of $x$ = 2.
The output value of $f(x)$ is 1, which corresponds to the input value of $x$ = 4.
The output value of $f(x)$ is 5, which corresponds to the input value of $x$ = 6.

Conclusion

Based on the given table, the inputs of the function are the values of $x$ that correspond to the output values of $f(x)$ . Therefore, the inputs of the function are -8, 2, 4, and 6.

Final Answer

The final answer is $\boxed{B}$ .

Discussion

The correct answer is B. The inputs of the function are the values of $x$ that correspond to the output values of $f(x)$ . In this case, the output values are -6, -3, 1, and 5, which correspond to the input values -8, 2, 4, and 6, respectively.

Related Concepts

This problem involves understanding the concept of functions and how to identify the inputs of a function based on a given table of values. It also requires the ability to match output values with their corresponding input values.

Example Use Cases

This problem can be used as an example in a mathematics or algebra class to teach students about functions and how to identify the inputs of a function. It can also be used to assess students' understanding of this concept.

Tips and Tricks

To solve this problem, students should carefully examine the table of values and match the output values with their corresponding input values. They should also make sure to read the table carefully and not make any assumptions about the values.

Common Mistakes

One common mistake students make when solving this problem is assuming that the output values are the inputs of the function. However, the output values are actually the values of $f(x)$ , and the inputs are the values of $x$ that correspond to these output values.

Conclusion

In conclusion, the inputs of the function are the values of $x$ that correspond to the output values of $f(x)$ . Based on the given table, the inputs of the function are -8, 2, 4, and 6.

Frequently Asked Questions

Q: What are the inputs of the function below?

A: The inputs of the function are the values of $x$ that correspond to the output values of $f(x)$ . In this case, the output values are -6, -3, 1, and 5, which correspond to the input values -8, 2, 4, and 6, respectively.

Q: How do I identify the inputs of a function?

A: To identify the inputs of a function, you need to match the output values with their corresponding input values in the table. Make sure to read the table carefully and not make any assumptions about the values.

Q: What is the difference between the output values and the input values?

A: The output values are the values of $f(x)$ , while the input values are the values of $x$ that correspond to these output values.

Q: Can you give an example of how to identify the inputs of a function?

A: Let's say we have a table with the following values:

$x$	-8	2	4	6
$f(x)$	-6	-3	1	5

To identify the inputs of the function, we need to match the output values with their corresponding input values. In this case, the output value -6 corresponds to the input value -8, the output value -3 corresponds to the input value 2, the output value 1 corresponds to the input value 4, and the output value 5 corresponds to the input value 6.

Q: What are some common mistakes to avoid when identifying the inputs of a function?

A: One common mistake is assuming that the output values are the inputs of the function. However, the output values are actually the values of $f(x)$ , and the inputs are the values of $x$ that correspond to these output values.

Q: How can I practice identifying the inputs of a function?

A: You can practice identifying the inputs of a function by working through examples like the one above. Make sure to read the table carefully and match the output values with their corresponding input values.

Q: What are some real-world applications of identifying the inputs of a function?

A: Identifying the inputs of a function is an important concept in mathematics and has many real-world applications, such as modeling population growth, predicting stock prices, and optimizing business processes.

Q: Can you give a tip for remembering how to identify the inputs of a function?

A: One tip is to remember that the input values are the values of $x$ that correspond to the output values of $f(x)$ . You can also try to visualize the function as a graph and identify the input values as the x-coordinates of the points on the graph.

Conclusion

In conclusion, identifying the inputs of a function is an important concept in mathematics that has many real-world applications. By understanding how to identify the inputs of a function, you can better analyze and solve problems in a variety of fields. Remember to match the output values with their corresponding input values and avoid common mistakes like assuming that the output values are the inputs of the function.