Which of the following is the same as the restricted-domain function𝑓(𝑥)=𝑖𝑛𝑡(𝑥),0≤𝑥<2

Question

(A) 𝑓(𝑥)={0𝑖𝑓0≤𝑥<11𝑖𝑓𝑥=12𝑖𝑓1<𝑥<2
(B) 𝑓(𝑥)={0𝑖𝑓𝑥=01𝑖𝑓0<𝑥≤12𝑖𝑓1<𝑥<2
(C) 𝑓(𝑥)={0𝑖𝑓0≤𝑥<11𝑖𝑓1≤𝑥<2
(D) 𝑓(𝑥)={0𝑖𝑓0≤𝑥<12𝑖𝑓1≤𝑥<2
(E)𝑓(𝑥)={𝑥𝑖𝑓0≤𝑥<11+𝑥𝑖𝑓1≤𝑥<2

Answer 1

I am trying to make sense of this. Perhaps you mean:
Which of the following is the same as the restricted-domain function𝑓(𝑥)=𝑖𝑛𝑡(𝑥),0≤𝑥<2

(A) 𝑓(𝑥)={0 𝑖𝑓 0≤𝑥<1 , 1 𝑖𝑓 𝑥=1 , 2 𝑖𝑓 1<𝑥<2
(B) 𝑓(𝑥)={0 𝑖𝑓 𝑥=0 , 1 𝑖𝑓 0<𝑥≤1 , 2 𝑖𝑓 1<𝑥<2
(C) 𝑓(𝑥)={0 𝑖𝑓 0≤𝑥<1 , 1 𝑖𝑓 1≤𝑥<2
(D) 𝑓(𝑥)={0 𝑖𝑓 0≤𝑥<1 , 2 𝑖𝑓 1≤𝑥<2
(E)𝑓(𝑥)={𝑥 𝑖𝑓 0≤𝑥<1 , 1+𝑥 𝑖𝑓 1≤𝑥<2

0 is 0 , It can round down to zero if between 0 and 1
1 is 1, it can round down to 1 between 1 and 2
looks like C