2) $f(x) = 5 + X$3) Complete The Table Using The Function $f(x) = 5 + X$:$\[ \begin{tabular}{|c|c|c|c|c|c|} \hline $x$ & -3 & -1 & 3 & 5 & 7 \\ \hline $f(x)$ & 2 & 4 & 8 & 10 & 12

Introduction

In mathematics, a linear function is a function that can be written in the form of $f(x) = mx + b$, where $m$ is the slope and $b$ is the y-intercept. In this article, we will be working with a linear function of the form $f(x) = 5 + x$. We will use this function to complete a table with given values of $x$.

Understanding the Function

The given function is $f(x) = 5 + x$. This means that for every value of $x$, we add 5 to it to get the corresponding value of $f(x)$. For example, if $x = 2$, then $f(x) = 5 + 2 = 7$.

Completing the Table

We are given a table with values of $x$ and corresponding values of $f(x)$. However, the values of $f(x)$ are not calculated using the function $f(x) = 5 + x$. We will use this function to calculate the correct values of $f(x)$ for each value of $x$.

x	f(x)
-3	2
-1	4
3	8
5	10
7	12

To complete the table, we will substitute each value of $x$ into the function $f(x) = 5 + x$ and calculate the corresponding value of $f(x)$.

Calculating f(x) for x = -3

$f(x) = 5 + x$ $f(-3) = 5 + (-3)$ $f(-3) = 5 - 3$ $f(-3) = 2$

Calculating f(x) for x = -1

$f(x) = 5 + x$ $f(-1) = 5 + (-1)$ $f(-1) = 5 - 1$ $f(-1) = 4$

Calculating f(x) for x = 3

$f(x) = 5 + x$ $f(3) = 5 + 3$ $f(3) = 5 + 3$ $f(3) = 8$

Calculating f(x) for x = 5

$f(x) = 5 + x$ $f(5) = 5 + 5$ $f(5) = 5 + 5$ $f(5) = 10$

Calculating f(x) for x = 7

$f(x) = 5 + x$ $f(7) = 5 + 7$ $f(7) = 5 + 7$ $f(7) = 12$

Completed Table

x	f(x)
-3	2
-1	4
3	8
5	10
7	12

Discussion

In this article, we used the linear function $f(x) = 5 + x$ to complete a table with given values of $x$. We calculated the corresponding values of $f(x)$ for each value of $x$ using the function. This demonstrates how to use a linear function to complete a table with given values.

Conclusion

In conclusion, completing a table using a linear function involves substituting each value of $x$ into the function and calculating the corresponding value of $f(x)$. This is a useful skill in mathematics, as it allows us to work with linear functions and complete tables with given values.

Example Problems

1. Complete the table using the function $f(x) = 2x + 1$:

x	f(x)
-2	3
0	1
4	9
6	13

2. Complete the table using the function $f(x) = -3x + 2$:

x	f(x)
-1	5
2	-4
5	-13
8	-22

Answer Key

1.	x	f(x)
-2	3
0	1
4	9
6	13

$f(-2) = 2(-2) + 1 = -3 + 1 = -2 + 3 = 1$ $f(0) = 2(0) + 1 = 0 + 1 = 1$ $f(4) = 2(4) + 1 = 8 + 1 = 9$ $f(6) = 2(6) + 1 = 12 + 1 = 13$

2.	x	f(x)
-1	5
2	-4
5	-13
8	-22

$$ $$ $$ $$

Introduction

In our previous article, we discussed how to complete a table using a linear function. We used the function $f(x) = 5 + x$ to complete a table with given values of $x$. In this article, we will answer some frequently asked questions about completing tables using linear functions.

Q: What is a linear function?

A linear function is a function that can be written in the form of $f(x) = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Q: How do I know if a function is linear?

To determine if a function is linear, you can check if it can be written in the form of $f(x) = mx + b$. If it can, then it is a linear function.

Q: What is the slope of a linear function?

The slope of a linear function is the coefficient of $x$ in the function. For example, in the function $f(x) = 2x + 1$, the slope is 2.

Q: What is the y-intercept of a linear function?

The y-intercept of a linear function is the value of $b$ in the function. For example, in the function $f(x) = 2x + 1$, the y-intercept is 1.

Q: How do I complete a table using a linear function?

To complete a table using a linear function, you need to substitute each value of $x$ into the function and calculate the corresponding value of $f(x)$.

Q: What if I have a table with values of $x$ and corresponding values of $f(x)$, but the values of $f(x)$ are not calculated using the function?

In this case, you can use the function to calculate the correct values of $f(x)$ for each value of $x$.

Q: Can I use a linear function to complete a table with negative values of $x$?

Yes, you can use a linear function to complete a table with negative values of $x$. The function will still work as long as the values of $x$ are in the domain of the function.

Q: Can I use a linear function to complete a table with decimal values of $x$?

Yes, you can use a linear function to complete a table with decimal values of $x$. The function will still work as long as the values of $x$ are in the domain of the function.

Q: How do I know if a table is completed correctly using a linear function?

To check if a table is completed correctly using a linear function, you can plug in the values of $x$ and $f(x)$ into the function and see if the equation holds true.

Q: What if I make a mistake when completing a table using a linear function?

If you make a mistake when completing a table using a linear function, you can go back and recheck your work. You can also use a calculator or a computer program to help you complete the table.

Conclusion

In conclusion, completing a table using a linear function is a useful skill in mathematics. By understanding the concept of linear functions and how to complete tables using them, you can solve a wide range of problems in mathematics and other fields.

Example Problems

1. Complete the table using the function $f(x) = 2x + 1$:

x	f(x)
-2	3
0	1
4	9
6	13

2. Complete the table using the function $f(x) = -3x + 2$:

x	f(x)
-1	5
2	-4
5	-13
8	-22

Answer Key

1.	x	f(x)
-2	3
0	1
4	9
6	13

$f(-2) = 2(-2) + 1 = -4 + 1 = -3 + 3 = 0$ $f(0) = 2(0) + 1 = 0 + 1 = 1$ $f(4) = 2(4) + 1 = 8 + 1 = 9$ $f(6) = 2(6) + 1 = 12 + 1 = 13$

2.	x	f(x)
-1	5
2	-4
5	-13
8	-22

$f(-1) = -3(-1) + 2 = 3 + 2 = 5$ $f(2) = -3(2) + 2 = -6 + 2 = -4$ $f(5) = -3(5) + 2 = -15 + 2 = -13$ $f(8) = -3(8) + 2 = -24 + 2 = -22$