Given:
[tex]f(x)=-4 \sqrt[3]{x}+6[/tex]
To find:
Which table shows correct values for the function.
Solution:
Substitute x = -8 in the function:
[tex]f(-8)=-4 \sqrt[3]{-8}+6[/tex]
Apply radical rule: [tex]\sqrt[n]{-a}=-\sqrt[n]{a}[/tex], if n is odd.
[tex]f(-8)=-(-4 \sqrt[3]{8})+6[/tex]
[tex]f(-8)=4 \sqrt[3]{2^3}+6[/tex]
[tex]f(-8)=4 (2)+6[/tex]
f(-8) = 14
Substitute x = -1 in the function:
[tex]f(-8)=-4 \sqrt[3]{-1}+6[/tex]
Apply radical rule: [tex]\sqrt[n]{-a}=-\sqrt[n]{a}[/tex], if n is odd.
[tex]f(-1)=-(-4 \sqrt[3]{1})+6[/tex]
[tex]f(-1)=4 \sqrt[3]{1^3}+6[/tex]
[tex]f(-1)=4 (1)+6[/tex]
f(-8) = 10
Substitute x = 0 in the function:
[tex]f(0)=-4 \sqrt[3]{0}+6[/tex]
[tex]f(0)=0+6[/tex]
f(0) = 6
Substitute x = 8 in the function:
[tex]f(8)=-4 \sqrt[3]{8}+6[/tex]
[tex]f(8)=-4 \sqrt[3]{2^3}+6[/tex]
[tex]f(8)=-4 (2)+6[/tex]
f(8) = -2
Therefore table 3 is shows correct values for the function.
