Given:
![f(x)=-4 \sqrt[3]{x}+6](https://tex.z-dn.net/?f=f%28x%29%3D-4%20%5Csqrt%5B3%5D%7Bx%7D%2B6)
To find:
Which table shows correct values for the function.
Solution:
Substitute x = -8 in the function:
![f(-8)=-4 \sqrt[3]{-8}+6](https://tex.z-dn.net/?f=f%28-8%29%3D-4%20%5Csqrt%5B3%5D%7B-8%7D%2B6)
Apply radical rule:
, if n is odd.
![f(-8)=-(-4 \sqrt[3]{8})+6](https://tex.z-dn.net/?f=f%28-8%29%3D-%28-4%20%5Csqrt%5B3%5D%7B8%7D%29%2B6)
![f(-8)=4 \sqrt[3]{2^3}+6](https://tex.z-dn.net/?f=f%28-8%29%3D4%20%5Csqrt%5B3%5D%7B2%5E3%7D%2B6)
![f(-8)=4 (2)+6](https://tex.z-dn.net/?f=f%28-8%29%3D4%20%282%29%2B6)
f(-8) = 14
Substitute x = -1 in the function:
![f(-8)=-4 \sqrt[3]{-1}+6](https://tex.z-dn.net/?f=f%28-8%29%3D-4%20%5Csqrt%5B3%5D%7B-1%7D%2B6)
Apply radical rule:
, if n is odd.
![f(-1)=-(-4 \sqrt[3]{1})+6](https://tex.z-dn.net/?f=f%28-1%29%3D-%28-4%20%5Csqrt%5B3%5D%7B1%7D%29%2B6)
![f(-1)=4 \sqrt[3]{1^3}+6](https://tex.z-dn.net/?f=f%28-1%29%3D4%20%5Csqrt%5B3%5D%7B1%5E3%7D%2B6)
![f(-1)=4 (1)+6](https://tex.z-dn.net/?f=f%28-1%29%3D4%20%281%29%2B6)
f(-8) = 10
Substitute x = 0 in the function:
![f(0)=-4 \sqrt[3]{0}+6](https://tex.z-dn.net/?f=f%280%29%3D-4%20%5Csqrt%5B3%5D%7B0%7D%2B6)
![f(0)=0+6](https://tex.z-dn.net/?f=f%280%29%3D0%2B6)
f(0) = 6
Substitute x = 8 in the function:
![f(8)=-4 \sqrt[3]{8}+6](https://tex.z-dn.net/?f=f%288%29%3D-4%20%5Csqrt%5B3%5D%7B8%7D%2B6)
![f(8)=-4 \sqrt[3]{2^3}+6](https://tex.z-dn.net/?f=f%288%29%3D-4%20%5Csqrt%5B3%5D%7B2%5E3%7D%2B6)
![f(8)=-4 (2)+6](https://tex.z-dn.net/?f=f%288%29%3D-4%20%282%29%2B6)
f(8) = -2
Therefore table 3 is shows correct values for the function.