Complete The Table Of Values For $f(x)=3x+8$ And $g(x)=8x^2-2$.$\[ \begin{tabular}{|c|l|l|} \hline $x$ & $f(x)$ & $g(x)$ \\ \hline 0 & $\square$ & $\square$ \\ \hline 1 & $\square$ & $\square$ \\ \hline 2 & $\square$ & $\square$

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 focus on completing the table of values for two given functions, $f(x)=3x+8$ and $g(x)=8x^2-2$. We will use these functions to calculate the values of $f(x)$ and $g(x)$ for different input values of $x$.

Understanding the Functions

Before we proceed, let's understand the two functions given to us.

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

This is a linear function, which means it has a constant rate of change. The function is defined as $f(x)=3x+8$, where $x$ is the input value and $f(x)$ is the output value. To calculate the value of $f(x)$, we simply multiply the input value $x$ by 3 and add 8.

Function $g(x)=8x^2-2$

This is a quadratic function, which means it has a parabolic shape. The function is defined as $g(x)=8x^2-2$, where $x$ is the input value and $g(x)$ is the output value. To calculate the value of $g(x)$, we square the input value $x$, multiply it by 8, and then subtract 2.

Completing the Table of Values

Now that we understand the two functions, let's complete the table of values for $f(x)$ and $g(x)$.

$x$	$f(x)$	$g(x)$
0	$\square$	$\square$
1	$\square$	$\square$
2	$\square$	$\square$

To complete the table, we need to calculate the values of $f(x)$ and $g(x)$ for each input value of $x$.

Calculating $f(x)$ for $x=0$

To calculate the value of $f(x)$ for $x=0$, we substitute $x=0$ into the function $f(x)=3x+8$. This gives us:

$f(0)=3(0)+8=8$

So, the value of $f(x)$ for $x=0$ is 8.

Calculating $f(x)$ for $x=1$

To calculate the value of $f(x)$ for $x=1$, we substitute $x=1$ into the function $f(x)=3x+8$. This gives us:

$f(1)=3(1)+8=11$

So, the value of $f(x)$ for $x=1$ is 11.

Calculating $f(x)$ for $x=2$

To calculate the value of $f(x)$ for $x=2$, we substitute $x=2$ into the function $f(x)=3x+8$. This gives us:

$f(2)=3(2)+8=14$

So, the value of $f(x)$ for $x=2$ is 14.

Calculating $g(x)$ for $x=0$

To calculate the value of $g(x)$ for $x=0$, we substitute $x=0$ into the function $g(x)=8x^2-2$. This gives us:

$g(0)=8(0)^2-2=-2$

So, the value of $g(x)$ for $x=0$ is -2.

Calculating $g(x)$ for $x=1$

To calculate the value of $g(x)$ for $x=1$, we substitute $x=1$ into the function $g(x)=8x^2-2$. This gives us:

$g(1)=8(1)^2-2=6$

So, the value of $g(x)$ for $x=1$ is 6.

Calculating $g(x)$ for $x=2$

To calculate the value of $g(x)$ for $x=2$, we substitute $x=2$ into the function $g(x)=8x^2-2$. This gives us:

$g(2)=8(2)^2-2=30$

So, the value of $g(x)$ for $x=2$ is 30.

Conclusion

In this article, we completed the table of values for two given functions, $f(x)=3x+8$ and $g(x)=8x^2-2$. We calculated the values of $f(x)$ and $g(x)$ for different input values of $x$ and filled in the table accordingly. This exercise helps us understand the behavior of the functions and how they change as the input value changes.

Final Table of Values

$x$	$f(x)$	$g(x)$
0	8	-2
1	11	6
2	14	30

Introduction

In our previous article, we completed the table of values for two given functions, $f(x)=3x+8$ and $g(x)=8x^2-2$. We calculated the values of $f(x)$ and $g(x)$ for different input values of $x$ and filled in the table accordingly. In this article, we will answer some frequently asked questions related to completing the table of values for given functions.

Q&A

Q: What is the purpose of completing the table of values for given functions?

A: The purpose of completing the table of values for given functions is to understand the behavior of the functions and how they change as the input value changes. It helps us visualize the relationship between the input and output values of the function.

Q: How do I know which values to use for the input variable x?

A: The values to use for the input variable x are usually given in the problem statement. If not, you can choose any values that are convenient for you to work with.

Q: Can I use any type of function to complete the table of values?

A: No, you cannot use any type of function to complete the table of values. The function must be defined and have a clear relationship between the input and output values.

Q: How do I calculate the values of f(x) and g(x) for different input values of x?

A: To calculate the values of f(x) and g(x) for different input values of x, you simply substitute the input value x into the function and perform the necessary calculations.

Q: What if I make a mistake while calculating the values of f(x) and g(x)?

A: If you make a mistake while calculating the values of f(x) and g(x), you can always go back and recheck your work. It's also a good idea to double-check your calculations with a calculator or by using a different method.

Q: Can I use technology to complete the table of values for given functions?

A: Yes, you can use technology such as calculators or computer software to complete the table of values for given functions. This can be especially helpful if you are working with complex functions or need to calculate many values.

Q: How do I know if I have completed the table of values correctly?

A: To know if you have completed the table of values correctly, you can check your work by using a calculator or by having someone else check your work. You can also use technology to check your work.

Common Mistakes to Avoid

When completing the table of values for given functions, there are several common mistakes to avoid. These include:

• Not following the order of operations: Make sure to follow the order of operations (PEMDAS) when calculating the values of f(x) and g(x).
• Not checking your work: Always check your work to make sure you have completed the table of values correctly.
• Using the wrong values for the input variable x: Make sure to use the correct values for the input variable x.
• Not using the correct function: Make sure to use the correct function when completing the table of values.

Conclusion

In this article, we answered some frequently asked questions related to completing the table of values for given functions. We also discussed some common mistakes to avoid when completing the table of values. By following these tips and avoiding common mistakes, you can ensure that you complete the table of values correctly and accurately.

Final Tips

• Practice, practice, practice: The more you practice completing the table of values for given functions, the more comfortable you will become with the process.
• Use technology: Technology can be a big help when completing the table of values for given functions.
• Check your work: Always check your work to make sure you have completed the table of values correctly.

I hope this article has been helpful in answering your questions about completing the table of values for given functions. If you have any further questions or need additional clarification, please feel free to ask.