Question

which function has the range (-infinity, 0]U[2, infinity)???

A. y=sec x
B. y= csc(x) + 1
C.y= cot(2x) - 1
D.y= cos(x+1)

Answer 1

its B

Answer 2

how??

Answer 3

csc(x)=1/sin(x)
and sin(x) has a range of (-1,1), so csc(x) has a range of \( (-inf,-1]\cup[1,+inf) \).
By adding 1 to csc(x), the range changes to \( (-inf,0]\cup[2,+inf) \).