Fill In The Table Of Values For The Function $f(x) = \sqrt[3]{x+2}$.$\[ \begin{array}{c|c} x & F(x) = \sqrt[3]{x+2} \\ \hline -3 & \\ -2 & \\ -1 & \\ 6 & \\ 1 & \\ -2 & \\ -1 & \\ 2 & \\ 3 & \\ 0 & \\ -3 &

Filling in the Table of Values for the Function $f(x) = \sqrt[3]{x+2}$

Understanding the Function

The given function is $f(x) = \sqrt[3]{x+2}$. This is a cubic root function, which means that it takes the cube root of the value inside the parentheses and adds 2 to it. The cube root of a number is a value that, when multiplied by itself twice (or cubed), gives the original number. For example, the cube root of 27 is 3, because 3 × 3 × 3 = 27.

Filling in the Table of Values

To fill in the table of values, we need to plug in the given values of x into the function and calculate the corresponding values of f(x). We will start by filling in the values of x and then calculate the values of f(x).

Step 1: Fill in the values of x

Step 2: Calculate the values of f(x)

To calculate the values of f(x), we need to plug in the values of x into the function and simplify.

• For x = -3, f(x) = ∛(-3+2) = ∛(-1) = -1
• For x = -2, f(x) = ∛(-2+2) = ∛0 = 0
• For x = -1, f(x) = ∛(-1+2) = ∛1 = 1
• For x = 6, f(x) = ∛(6+2) = ∛8 = 2
• For x = 1, f(x) = ∛(1+2) = ∛3 = 1.4422 (approximately)
• For x = -2, f(x) = ∛(-2+2) = ∛0 = 0
• For x = -1, f(x) = ∛(-1+2) = ∛1 = 1
• For x = 2, f(x) = ∛(2+2) = ∛4 = 1.5874 (approximately)
• For x = 3, f(x) = ∛(3+2) = ∛5 = 1.7090 (approximately)
• For x = 0, f(x) = ∛(0+2) = ∛2 = 1.2599 (approximately)
• For x = -3, f(x) = ∛(-3+2) = ∛(-1) = -1

Step 3: Fill in the table of values

Conclusion

In this article, we filled in the table of values for the function $f(x) = \sqrt[3]{x+2}$. We started by understanding the function and then filled in the values of x and calculated the corresponding values of f(x). The table of values is now complete, and we can use it to visualize the behavior of the function.

Key Takeaways

• The function $f(x) = \sqrt[3]{x+2}$ is a cubic root function that takes the cube root of the value inside the parentheses and adds 2 to it.
• To fill in the table of values, we need to plug in the given values of x into the function and calculate the corresponding values of f(x).
• The table of values can be used to visualize the behavior of the function and understand its properties.

Further Reading

If you want to learn more about functions and how to fill in tables of values, I recommend checking out the following resources:

• Khan Academy: Functions and Graphs
• Mathway: Functions and Graphs
• Wolfram Alpha: Functions and Graphs

I hope this article has been helpful in filling in the table of values for the function $f(x) = \sqrt[3]{x+2}$. If you have any questions or need further clarification, please don't hesitate to ask.
Filling in the Table of Values for the Function $f(x) = \sqrt[3]{x+2}$: Q&A

Understanding the Function

The given function is $f(x) = \sqrt[3]{x+2}$. This is a cubic root function, which means that it takes the cube root of the value inside the parentheses and adds 2 to it. The cube root of a number is a value that, when multiplied by itself twice (or cubed), gives the original number. For example, the cube root of 27 is 3, because 3 × 3 × 3 = 27.

Filling in the Table of Values

To fill in the table of values, we need to plug in the given values of x into the function and calculate the corresponding values of f(x). We will start by filling in the values of x and then calculate the values of f(x).

Q: What is the cube root function?

A: The cube root function is a mathematical function that takes the cube root of a number. It is denoted by the symbol ∛ and is used to find the value that, when multiplied by itself twice (or cubed), gives the original number.

Q: How do I fill in the table of values for the function $f(x) = \sqrt[3]{x+2}$?

A: To fill in the table of values, you need to plug in the given values of x into the function and calculate the corresponding values of f(x). You can use a calculator or a computer program to help you with the calculations.

Q: What is the value of f(x) when x = -3?

A: When x = -3, f(x) = ∛(-3+2) = ∛(-1) = -1.

Q: What is the value of f(x) when x = 6?

A: When x = 6, f(x) = ∛(6+2) = ∛8 = 2.

Q: How do I calculate the values of f(x) for the given values of x?

A: To calculate the values of f(x), you need to plug in the values of x into the function and simplify. You can use a calculator or a computer program to help you with the calculations.

Q: What is the table of values for the function $f(x) = \sqrt[3]{x+2}$?

A: The table of values for the function $f(x) = \sqrt[3]{x+2}$ is:

Conclusion

In this article, we answered some common questions about filling in the table of values for the function $f(x) = \sqrt[3]{x+2}$. We covered topics such as the cube root function, how to fill in the table of values, and how to calculate the values of f(x) for the given values of x. We also provided a table of values for the function $f(x) = \sqrt[3]{x+2}$.

Key Takeaways

• The cube root function is a mathematical function that takes the cube root of a number.
• To fill in the table of values, you need to plug in the given values of x into the function and calculate the corresponding values of f(x).
• The table of values can be used to visualize the behavior of the function and understand its properties.

Further Reading

If you want to learn more about functions and how to fill in tables of values, I recommend checking out the following resources:

• Khan Academy: Functions and Graphs
• Mathway: Functions and Graphs
• Wolfram Alpha: Functions and Graphs

I hope this article has been helpful in answering your questions about filling in the table of values for the function $f(x) = \sqrt[3]{x+2}$. If you have any further questions or need further clarification, please don't hesitate to ask.