The Function Table of Values

Oct 13, 2025 by thesweetdesigns.com 140 views

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.

$x$	1	2	3	4	5
$f(x)$	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 $x$ increases, the output value $f(x)$ 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 $f(1)$ ?

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

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

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

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

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

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

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

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

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

Conclusion

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

References

[1] Khan Academy. (n.d.). Functions. Retrieved from https://www.khanacademy.org/math/algebra/x2f1f1/x2f1f2
[2] Math Open Reference. (n.d.). Functions. Retrieved from https://www.mathopenref.com/functions.html

Additional Resources

[1] Wolfram MathWorld. (n.d.). Function. Retrieved from https://mathworld.wolfram.com/Function.html
[2] MIT OpenCourseWare. (n.d.). 18.01 Single Variable Calculus. Retrieved from https://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2006/
Q&A: Understanding the Function and Selecting the Correct Answer ====================================================================

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 $f(1)$ ?

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

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

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

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

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

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

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

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

A: The value of $f(5)$ 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 $x$ increases, the output value $f(x)$ 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 $f(x)$ for each input value $x$ .

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.