Question

Which is the graph of the step function f(x)?

Answer 1

To determine the graph of the function f(x), consider such steps:

1 step. Since $f(x)=-1$ for all $x<-1,$ then you should take all points from the line $y=-1$ for which $x<-1$ - that is the left part of the line and point with x-coordinate -1 must be unfilled, because the sign is <.

2 step. Since $f(x)=0$ for all $-1\le x\le 1,$ then you should take all points from the line $y=0$ for which $-1\le x\le 1$ - that is the segment part of the line and points with x-coordinate -1 and 1  must be filled, because the signs are with notion "or equal to".

3 step. Since $f(x)=1$ for all $x>1,$ then you should take all points from the line $y=1$ for which $x>1$ - that is the right part of the line and point with x-coordinate 1 must be unfilled, because the sign is >.

Answer: correct choice is B

Answer 2

Answer:

Indeed

1 step. Since  for all  then you should take all points from the line  for which  - that is the left part of the line and point with x-coordinate -1 must be unfilled, because the sign is <.

2 step. Since  for all  then you should take all points from the line  for which  - that is the segment part of the line and points with x-coordinate -1 and 1  must be filled, because the signs are with notion "or equal to".

3 step. Since  for all  then you should take all points from the line  for which  - that is the right part of the line and point with x-coordinate 1 must be unfilled, because the sign is >.

Answer: correct choice is B