Piecewise Function Definitions - I

Answer the following question based on the information given below.

f₁(x) = x                  0 ≤ x ≤ 1
= 1                   x ≥ 1
= 0                   otherwise

f₂(x) = f₁(–x)           for all x
f₃(x) = –f₂(x)           for all x
f₄(x) = f₃(–x)           for all x

How many of the following products are necessarily zero for every x

f₁(x)f₂(x), f₂(x)f₃(x), f₂(x)f₄(x)?

SELECT ONE OPTION