Fill In The \[$ Y \$\] Values Of The \[$ T \$\]-table For The Function \[$ Y=\sqrt[3]{x} \$\].$\[ \begin{tabular}{c|l} $x$ & $y$ \\ \hline -8 & \\ -1 & \\ 0 & $\square$ \\ 1 & $\square$ \\ 8 & $\square$
Filling in the Values of the t-table for the Function y=³√x
Understanding the Function y=³√x
The function y=³√x represents the cube root of x. This means that for any given value of x, the corresponding value of y is the number that, when cubed, gives x. In other words, y³ = x.
Creating a t-table for the Function y=³√x
A t-table is a table that shows the values of x and the corresponding values of y for a given function. To create a t-table for the function y=³√x, we need to fill in the values of y for the given values of x.
Filling in the Values of y
To fill in the values of y, we need to cube each value of x and find the cube root of the result.
- For x = -8, we have y³ = -8. Taking the cube root of both sides, we get y = -2.
- For x = -1, we have y³ = -1. Taking the cube root of both sides, we get y = -1.
- For x = 0, we have y³ = 0. Taking the cube root of both sides, we get y = 0.
- For x = 1, we have y³ = 1. Taking the cube root of both sides, we get y = 1.
- For x = 8, we have y³ = 8. Taking the cube root of both sides, we get y = 2.
The Completed t-table
| x | y |
|---|---|
| -8 | -2 |
| -1 | -1 |
| 0 | 0 |
| 1 | 1 |
| 8 | 2 |
Discussion
The t-table for the function y=³√x shows the values of x and the corresponding values of y. This table can be used to help us understand the behavior of the function and to make predictions about the values of y for different values of x.
Key Takeaways
- The function y=³√x represents the cube root of x.
- To create a t-table for the function y=³√x, we need to fill in the values of y for the given values of x.
- The values of y can be found by cubing each value of x and taking the cube root of the result.
- The completed t-table shows the values of x and the corresponding values of y.
Conclusion
In this article, we have filled in the values of the t-table for the function y=³√x. We have also discussed the behavior of the function and how to use the t-table to make predictions about the values of y for different values of x.
Frequently Asked Questions (FAQs) about the Function y=³√x
Q: What is the function y=³√x?
A: The function y=³√x represents the cube root of x. This means that for any given value of x, the corresponding value of y is the number that, when cubed, gives x. In other words, y³ = x.
Q: How do I create a t-table for the function y=³√x?
A: To create a t-table for the function y=³√x, you need to fill in the values of y for the given values of x. You can do this by cubing each value of x and taking the cube root of the result.
Q: What is the difference between the cube root and the square root?
A: The cube root and the square root are both types of roots, but they are different. The square root of a number is the number that, when multiplied by itself, gives the original number. The cube root of a number is the number that, when cubed, gives the original number.
Q: Can I use the t-table to make predictions about the values of y for different values of x?
A: Yes, you can use the t-table to make predictions about the values of y for different values of x. By looking at the values of x and y in the table, you can see how the function behaves and make predictions about the values of y for different values of x.
Q: What are some real-world applications of the function y=³√x?
A: The function y=³√x has many real-world applications, including:
- Calculating the volume of a cube
- Finding the length of a side of a cube
- Determining the number of cubes that can fit in a given volume
- Calculating the surface area of a cube
Q: Can I use the function y=³√x to solve equations?
A: Yes, you can use the function y=³√x to solve equations. By substituting the values of x and y into the equation, you can solve for the unknown value.
Q: What are some common mistakes to avoid when working with the function y=³√x?
A: Some common mistakes to avoid when working with the function y=³√x include:
- Confusing the cube root with the square root
- Not cubing the values of x correctly
- Not taking the cube root of the result correctly
- Not using the correct values of x and y in the t-table
Q: Can I use a calculator to find the values of y for the function y=³√x?
A: Yes, you can use a calculator to find the values of y for the function y=³√x. Most calculators have a cube root function that you can use to find the values of y.
Q: What are some tips for memorizing the function y=³√x?
A: Some tips for memorizing the function y=³√x include:
- Writing the function down multiple times
- Creating a flashcard with the function on one side and the definition on the other
- Practicing the function with different values of x
- Using visual aids, such as graphs or charts, to help you remember the function
Conclusion
In this article, we have answered some frequently asked questions about the function y=³√x. We have discussed the definition of the function, how to create a t-table, and some real-world applications of the function. We have also provided some tips for memorizing the function and avoiding common mistakes.