Question

use the tables to answer the question.
table of x
and f(x)
values

x	f(x)
-4	-64
-3	-27
-2	-8

table of x
and h(x)
values

x	h(x)
1	-64
?	-27
3	-8

given the function f(x) in the first table, create a table for the function h(x) = (x - 5)^3 and then fill in the missing value in the table of h(x).
(1 point)

Explanation:

Step1: Analyze f(x) pattern

From the first table, observe that \( f(x)=x^{3} \) (since \((-4)^{3}=-64\), \((-3)^{3}=-27\), \((-2)^{3}=-8\)).

Step2: Relate h(x) to f(x)

Given \( h(x)=(x - 5)^{3} \), we want to find \( x \) when \( h(x)=-27 \). Let \( h(x)=-27 \), so \((x - 5)^{3}=-27\).

Step3: Solve for x

Take cube root on both sides: \( x - 5=\sqrt[3]{-27}=-3 \). Then \( x=-3 + 5 = 2 \).

Answer:

2