Select The Correct Answer From Each Drop-down Menu.The Function \[$ F \$\] Is Given By The Table Of Values As Shown Below.$\[ \begin{tabular}{|c|c|c|c|c|c|} \hline $x$ & 1 & 2 & 3 & 4 & 5 \\ \hline $f(x)$ & 13 & 19 & 37 & 91 & 253

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Introduction

In mathematics, functions are used to describe the relationship between variables. A function is a rule that assigns to each input value, or element, in a set called the domain, a unique output value, or element, in a set called the range. In this article, we will explore a given function { f $}$ and use a table of values to determine the correct answer from each drop-down menu.

The Function Table of Values

The function { f $}$ is given by the table of values as shown below.

xx 1 2 3 4 5
f(x)f(x) 13 19 37 91 253

Analyzing the Function

To understand the function, we need to analyze the table of values. We can see that as the input value xx increases, the output value f(x)f(x) also increases. This suggests that the function is an increasing function.

Determining the Correct Answer

To determine the correct answer from each drop-down menu, we need to examine the table of values and identify the pattern of the function.

Question 1: What is the value of f(1)f(1)?

The value of f(1)f(1) is given in the table of values as 13.

Question 2: What is the value of f(2)f(2)?

The value of f(2)f(2) is given in the table of values as 19.

Question 3: What is the value of f(3)f(3)?

The value of f(3)f(3) is given in the table of values as 37.

Question 4: What is the value of f(4)f(4)?

The value of f(4)f(4) is given in the table of values as 91.

Question 5: What is the value of f(5)f(5)?

The value of f(5)f(5) is given in the table of values as 253.

Conclusion

In conclusion, the function { f $}$ is an increasing function, and the values of f(x)f(x) for x=1,2,3,4,5x = 1, 2, 3, 4, 5 are 13, 19, 37, 91, and 253, respectively.

Discussion Category: Mathematics

This article is categorized under mathematics, as it deals with the analysis and understanding of a given function.

Key Takeaways

  • A function is a rule that assigns to each input value, or element, in a set called the domain, a unique output value, or element, in a set called the range.
  • The function { f $}$ is an increasing function, meaning that as the input value xx increases, the output value f(x)f(x) also increases.
  • The values of f(x)f(x) for x=1,2,3,4,5x = 1, 2, 3, 4, 5 are 13, 19, 37, 91, and 253, respectively.

References

Additional Resources

Introduction

In our previous article, we explored a given function { f $}$ and used a table of values to determine the correct answer from each drop-down menu. In this article, we will answer some frequently asked questions related to the function and provide additional insights.

Q&A

Q: What is the definition of a function?

A: A function is a rule that assigns to each input value, or element, in a set called the domain, a unique output value, or element, in a set called the range.

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

A: A relation is a set of ordered pairs, while a function is a relation where each input value corresponds to a unique output value.

Q: How do we determine if a function is increasing or decreasing?

A: We can determine if a function is increasing or decreasing by examining the table of values or by using the derivative of the function.

Q: What is the value of f(1)f(1)?

A: The value of f(1)f(1) is given in the table of values as 13.

Q: What is the value of f(2)f(2)?

A: The value of f(2)f(2) is given in the table of values as 19.

Q: What is the value of f(3)f(3)?

A: The value of f(3)f(3) is given in the table of values as 37.

Q: What is the value of f(4)f(4)?

A: The value of f(4)f(4) is given in the table of values as 91.

Q: What is the value of f(5)f(5)?

A: The value of f(5)f(5) is given in the table of values as 253.

Q: Is the function { f $}$ an increasing function?

A: Yes, the function { f $}$ is an increasing function, meaning that as the input value xx increases, the output value f(x)f(x) also increases.

Q: How do we use the table of values to determine the correct answer from each drop-down menu?

A: We can use the table of values to determine the correct answer from each drop-down menu by examining the values of f(x)f(x) for each input value xx.

Q: What are some real-world applications of functions?

A: Functions have many real-world applications, including modeling population growth, predicting stock prices, and optimizing business decisions.

Conclusion

In conclusion, the function { f $}$ is an increasing function, and the values of f(x)f(x) for x=1,2,3,4,5x = 1, 2, 3, 4, 5 are 13, 19, 37, 91, and 253, respectively. We hope that this Q&A article has provided additional insights and helped to clarify any questions you may have had.

Discussion Category: Mathematics

This article is categorized under mathematics, as it deals with the analysis and understanding of a given function.

Key Takeaways

  • A function is a rule that assigns to each input value, or element, in a set called the domain, a unique output value, or element, in a set called the range.
  • The function { f $}$ is an increasing function, meaning that as the input value xx increases, the output value f(x)f(x) also increases.
  • The values of f(x)f(x) for x=1,2,3,4,5x = 1, 2, 3, 4, 5 are 13, 19, 37, 91, and 253, respectively.

References

Additional Resources