Chapter 3, Exploration 20

For the chosen value of $$a$$ in the dropdown menu, the function $$s_a(x) = a \sin(x)$$ is shown below. The slider is above the graph and will adjust the initial condition $$x_0$$. Use this to determine the values of $$a$$ where the fixed point at $$x = 0$$ is attracting, repelling, or neither. What is this relationship between the graph of $$s_a(x)$$ and the the line $$y=x$$ near $$x = 0$$ when the fixed point is attracting versus when it is repelling?