Answer:
The degree of the power function is 3
Step-by-step explanation:
Let the power function be f(x) = b × xᵃ
Therefore, from the table, we have;
40 = b × (-2)ᵃ
5 = b × (-1)ᵃ
0 = b × 0ᵃ
-5 = b × (1)ᵃ
-40 = b × (2)ᵃ
From -5 = b × (1)ᵃ, we have;
1ᵃ = 1, which gives;
-5 = b × 1
b = -5
From -40 = b × (2)ᵃ, where b = -5, we have;
-40 = -5 × (2)ᵃ
(2)ᵃ = -40/(-5) = 8
(2)ᵃ = 8 = (2)³
∴ a = 3
㏑(2)ᵃ = ㏑(8)
a·㏑(2) = ㏑(8)
a = ㏑(8)/(㏑(2)) = 3
a = 3
The power function is f(x) = -5 × x³
∴ The degree of the power function is 3.
