Answer:
The graph of the step function f(x) is represented by the 2nd graph.
Step-by-step explanation:
We are given the step function,
[tex]\left\{\begin{matrix} -1,&x<-1 \\ 0, & -1<x<1 \\ 1, & x>1\end{matrix}\right.[/tex].
So, from the options, we see that,
In 1st graph, the conditions [tex]f(x)=-1,x<-1[/tex] and [tex]f(x)=1,x>1[/tex] is not satisfied.
In 3rd graph, the points -1,0,1 are included, which is not correct.
In 4th graph, [tex]f(x)=-1,x<-1[/tex] and [tex]f(x)=1,x>1[/tex] is not satisfied.
Thus, we have,
The graph of the step function f(x) is represented by the 2nd graph as shown below.
