Answer:
We are asked to graph the function:
f(x)= sin x ; if x≤ 0
and |x| ; if x > 0
We know that the function |x| is evaluated as:
|x|= -x ; if x≤0
and x ; if x > 0
Hence, we have to graph the function:
f(x) = sin x ; if x ≤ 0
and x ; if x > 0
Also the function is continuous at x=0.
Since the Left hand limit and the right hand limit of the function exist and is equal to the value of the function at x=0.
i.e. f(0)=0.
The graph is plotted as the graph of sin (x) in the region (-∞,0] and y=x in the region (0,∞).