Complete The Table Using The Function 2 N + 5 2n + 5 2 N + 5 . \[ \begin{tabular}{|c|c|} \hline In & Out \\ \hline N$ & 2 N + 5 2n + 5 2 N + 5 \ \hline 1 & \ \hline 2 & \ \hline 3 & \ \hline 4 & \ \hline 5 &

Introduction

In mathematics, functions are a fundamental concept that help us describe relationships between variables. A function is a rule that assigns to each input a unique output. In this article, we will explore the function $2n + 5$ and complete a table using this function.

The Function $2n + 5$

The function $2n + 5$ is a linear function, which means that it has a constant rate of change. The function takes an input value $n$ and returns an output value that is twice the input value plus 5.

Completing the Table

We are given a table with input values $n$ and output values $2n + 5$. We need to complete the table by filling in the missing output values.

In	Out
$n$	$2n + 5$
1
2
3
4
5

To complete the table, we can simply plug in the input values into the function $2n + 5$.

For $n = 1$

We substitute $n = 1$ into the function $2n + 5$:

$$2(1) + 5 = 2 + 5 = 7$$

So, the output value for $n = 1$ is 7.

For $n = 2$

We substitute $n = 2$ into the function $2n + 5$:

$$2(2) + 5 = 4 + 5 = 9$$

So, the output value for $n = 2$ is 9.

For $n = 3$

We substitute $n = 3$ into the function $2n + 5$:

$$2(3) + 5 = 6 + 5 = 11$$

So, the output value for $n = 3$ is 11.

For $n = 4$

We substitute $n = 4$ into the function $2n + 5$:

$$2(4) + 5 = 8 + 5 = 13$$

So, the output value for $n = 4$ is 13.

For $n = 5$

We substitute $n = 5$ into the function $2n + 5$:

$$2(5) + 5 = 10 + 5 = 15$$

So, the output value for $n = 5$ is 15.

Completed Table

Here is the completed table:

In	Out
$n$	$2n + 5$
1	7
2	9
3	11
4	13
5	15

Discussion

The function $2n + 5$ is a simple linear function that takes an input value $n$ and returns an output value that is twice the input value plus 5. We completed a table using this function by plugging in the input values into the function.

Conclusion

In this article, we explored the function $2n + 5$ and completed a table using this function. We learned how to plug in input values into the function to get the corresponding output values. This is a fundamental concept in mathematics that helps us understand relationships between variables.

Mathematical Exploration

The function $2n + 5$ can be used to model real-world situations, such as:

• A company that charges a base fee of $5 plus a rate of $2 per unit sold.
• A person who earns a base salary of $5 plus a rate of $2 per hour worked.

In both cases, the function $2n + 5$ can be used to calculate the total cost or earnings.

Real-World Applications

The function $2n + 5$ has many real-world applications, such as:

• Business: A company that charges a base fee of $5 plus a rate of $2 per unit sold can use the function $2n + 5$ to calculate the total cost of producing a certain number of units.
• Finance: A person who earns a base salary of $5 plus a rate of $2 per hour worked can use the function $2n + 5$ to calculate their total earnings for a certain number of hours worked.
• Science: A scientist who needs to calculate the total cost of a certain experiment can use the function $2n + 5$ to calculate the total cost based on the number of units used.

Conclusion

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Introduction

In our previous article, we explored the function $2n + 5$ and completed a table using this function. In this article, we will answer some frequently asked questions about the function $2n + 5$.

Q: What is the function $2n + 5$?

A: The function $2n + 5$ is a linear function that takes an input value $n$ and returns an output value that is twice the input value plus 5.

Q: How do I complete a table using the function $2n + 5$?

A: To complete a table using the function $2n + 5$, you simply plug in the input values into the function. For example, if you want to find the output value for $n = 3$, you would substitute $n = 3$ into the function $2n + 5$ and calculate the result.

Q: What are some real-world applications of the function $2n + 5$?

A: The function $2n + 5$ has many real-world applications, such as:

• Business: A company that charges a base fee of $5 plus a rate of $2 per unit sold can use the function $2n + 5$ to calculate the total cost of producing a certain number of units.
• Finance: A person who earns a base salary of $5 plus a rate of $2 per hour worked can use the function $2n + 5$ to calculate their total earnings for a certain number of hours worked.
• Science: A scientist who needs to calculate the total cost of a certain experiment can use the function $2n + 5$ to calculate the total cost based on the number of units used.

Q: How do I graph the function $2n + 5$?

A: To graph the function $2n + 5$, you can use a graphing calculator or a computer program. You can also plot points on a coordinate plane and draw a line through the points to create the graph.

Q: What is the domain and range of the function $2n + 5$?

A: The domain of the function $2n + 5$ is all real numbers, and the range is also all real numbers.

Q: Can I use the function $2n + 5$ to model other real-world situations?

A: Yes, you can use the function $2n + 5$ to model other real-world situations, such as:

• A company that charges a base fee of $5 plus a rate of $2 per unit sold
• A person who earns a base salary of $5 plus a rate of $2 per hour worked
• A scientist who needs to calculate the total cost of a certain experiment

Q: How do I determine if the function $2n + 5$ is a linear function?

A: To determine if the function $2n + 5$ is a linear function, you can check if the function has a constant rate of change. If the function has a constant rate of change, then it is a linear function.

Conclusion

In this article, we answered some frequently asked questions about the function $2n + 5$. We explored the function's definition, how to complete a table using the function, real-world applications, graphing the function, domain and range, and more. This is a fundamental concept in mathematics that helps us understand relationships between variables.

Mathematical Exploration

The function $2n + 5$ can be used to model real-world situations, such as:

• A company that charges a base fee of $5 plus a rate of $2 per unit sold
• A person who earns a base salary of $5 plus a rate of $2 per hour worked
• A scientist who needs to calculate the total cost of a certain experiment

In each of these situations, the function $2n + 5$ can be used to calculate the total cost or earnings.

Real-World Applications

The function $2n + 5$ has many real-world applications, such as:

• Business: A company that charges a base fee of $5 plus a rate of $2 per unit sold can use the function $2n + 5$ to calculate the total cost of producing a certain number of units.
• Finance: A person who earns a base salary of $5 plus a rate of $2 per hour worked can use the function $2n + 5$ to calculate their total earnings for a certain number of hours worked.
• Science: A scientist who needs to calculate the total cost of a certain experiment can use the function $2n + 5$ to calculate the total cost based on the number of units used.

Conclusion

In conclusion, the function $2n + 5$ is a simple linear function that takes an input value $n$ and returns an output value that is twice the input value plus 5. We answered some frequently asked questions about the function and explored its real-world applications. This is a fundamental concept in mathematics that helps us understand relationships between variables.