Math question, please?

Question

Let k = 1/x, if x<-1; and sin( (2xpi)/2), if -1<x<1; and 3-x, if x>or= 1

Find the domain and range, compute k(0) and describe the behavior of k(x) for values x close to -1

Answer 1

1. (-1,0)

2. (0,1]

3. [2,infinity)

Giving a range of (-1,1]\{0} u [2,infinity]

the function has R\{-1}

k(0)=1

As x approaches -1 from above k(x) approaches zero from the positive direction and k(x) behaves like y=x+1

As x approaches -1 from below k(x) approaches -1 from the negative direction and k(x) behaves like x=-1.