Question

Evaluate this piecewise function at x=-8 and x=8.

f(x) = { x³, if x < 0
{ ∛x, if x > 0
a) ƒ(–8) = –512; ƒ(8) = 2
b) nƒ(–8) = –24; ƒ(8) = 2
c) ƒ(–8) = –2; ƒ(8) = 512
d) ƒ(–8) = 512; ƒ(8) = 2

Answer 1

To evaluate the piecewise function at x=-8 and x=8, we use the respective conditions and find the corresponding values using the given function. The correct answer is a) ƒ(–8) = –512; ƒ(8) = 2.

Step-by-step explanation:

To evaluate the piecewise function at x=-8 and x=8, we need to consider the conditions for each case:

1. For x=-8, since x<0, we use the first part of the function, which is f(x) = x³. Plugging in x=-8, we get f(-8) = (-8)³ = -512.
2. For x=8, since x>0, we use the second part of the function, which is f(x) = ∛x. Plugging in x=8, we get f(8) = ∛8 = 2.

Therefore, the correct answer is a) ƒ(–8) = –512; ƒ(8) = 2.