Question

Consider the following function. Which table shows correct values for the function?

Answer 1

Given:

$f(x)=-4 \sqrt[3]{x}+6$

To find:

Which table shows correct values for the function.

Solution:

Substitute x = -8 in the function:

$f(-8)=-4 \sqrt[3]{-8}+6$

Apply radical rule: $\sqrt[n]{-a}=-\sqrt[n]{a}$, if n is odd.

$f(-8)=-(-4 \sqrt[3]{8})+6$

$f(-8)=4 \sqrt[3]{2^3}+6$

$f(-8)=4 (2)+6$

f(-8) = 14

Substitute x = -1 in the function:

$f(-8)=-4 \sqrt[3]{-1}+6$

Apply radical rule: $\sqrt[n]{-a}=-\sqrt[n]{a}$, if n is odd.

$f(-1)=-(-4 \sqrt[3]{1})+6$

$f(-1)=4 \sqrt[3]{1^3}+6$

$f(-1)=4 (1)+6$

f(-8) = 10

Substitute x = 0 in the function:

$f(0)=-4 \sqrt[3]{0}+6$

$f(0)=0+6$

f(0) = 6

Substitute x = 8 in the function:

$f(8)=-4 \sqrt[3]{8}+6$

$f(8)=-4 \sqrt[3]{2^3}+6$

$f(8)=-4 (2)+6$

f(8) = -2

Therefore table 3 is shows correct values for the function.