Answer:
I can fill in the table for the function \(f(x) = 3\sqrt{x}\). However, it's important to note that this function is not defined for negative values of \(x\) (like -8 and -1), as you cannot calculate the square root of a negative number in the real number system. Here is the completed table:
X - Y
-8 ? Not defined
-1 ? Not defined
0 ? 0
1 ? 3
8 ? 9
The image you sent shows a different function, \(f(x) = \sqrt[3]{x}\), which is the cube root function. This function is defined for all values of \(x\), and has a different shape and behavior than the square root function. To fill in the table for the cube root function, you need to find the value of \(x\) that is raised to the power of 3 to get the corresponding value of \(y\). For example, \(\sqrt[3]{8} = 2\), because \(2^3 = 8\). Here is the completed table for the cube root function:
X - Y
-8 ? -2
-1 ? -1
0 ? 0
1 ? 1
8 ? 2
I hope this helps you understand the difference between the square root and the cube root functions.
