Answer:
The correct option is C. [tex]y=\left \{ {x^2+4, \; x<2} \atop {x+4, \;x\geq 2}} \right.[/tex]
Step-by-step explanation:
Consider the provided graph:
The graph has an open and closed dot at x = 2.
The open dot attached to the function [tex]y=x^{2}+4[/tex] and the closed dot attached to the function [tex]y=x+4[/tex].
Note, we use [tex]\leq or \geq[/tex] sign in order to show closed dots and < or > sign to show open dots.
By observing the graph, it is clear that the function [tex]y=x+4[/tex] takes all the value which are greater or equal to 2. Therefore, the function can be written as [tex]y=x+4, x\geq 2[/tex].
The graph of the function [tex]y=x^{2}+4[/tex] has an open dot at [tex]x = 2[/tex] which means the function can take all real values less than 2. Therefore, the function can be written as [tex]x^2+4, x<2[/tex].
Therefore, the correct option is C. [tex]y=\left \{ {x^2+4, \; x<2} \atop {x+4, \;x\geq 2}} \right.[/tex]
