Answer:
Option C is correct.
Explanation:
A piece-wise function is a function which is defined by multiple sub-functions, each sub-function applying to a certain interval of the main function's domain.
From the graph we can see that the function is made up of 2 pieces.
Solid dot means- Including
Open-dot means - not- including.
As we can see that the boundary lines are at x=1.
We have to look each line separately to determine each equation:
when [tex]x>1[/tex], it gives the function [tex]y=x^2+4[/tex] and
when [tex]x\leq 1[/tex], it gives the function [tex]y =x^3-2[/tex].
So, the piece-wise function is:
[tex]y=\left \{ {{x^3-2}, x\leq1 \atop {x^2+4}, x>1} \right.[/tex]
