Given:
The graph of a function [tex]y=h(x)[/tex].
To find:
The interval where [tex]h(x)>0[/tex].
Solution:
From the given graph graph it is clear that, the function before x=0 and after x=3.6 lies above the x-axis. So, [tex]h(x)>0[/tex] for [tex]x<0[/tex] and [tex]x>3.6[/tex].
The function between x=0 and x=3.6 lies below the x-axis. So, [tex]h(x)<0[/tex] for [tex]0<x<3.6[/tex].
Now,
For [tex]-1<x<0[/tex], the graph of h(x) is above the x-axis. So, [tex]h(x)>0[/tex].
For [tex]0<x<1[/tex], the graph of h(x) is below the x-axis. So, [tex]h(x)<0[/tex].
For [tex]1<x<2[/tex], the graph of h(x) is below the x-axis. So, [tex]h(x)<0[/tex].
Only for the interval [tex]-1<x<0[/tex], we get [tex]h(x)>0[/tex].
Therefore, the correct option is A.
