Answer:
[tex]y=\begin{cases}x^3-3 & \text{ if } x\le 2 \\ x^2+6 & \text{ if } x>2 \end{cases}[/tex]
Step-by-step explanation:
The given graph represents a piecewise function. The graph is discontinuous at x=2.
Open circle represents that the point x=2 is not included in the function and closed circle represents that the point x=2 is included in the function.
For x≤2, it a the graph of a cubic function which is generated by shifting the graph of [tex]y=x^3[/tex] to three units down.
[tex]y=x^3-3[/tex] for x≤2
For x>2, it a the graph of a quadratic function which is generated by shifting the graph of [tex]y=x^2[/tex] to 6 units up.
[tex]y=x^2+6[/tex] for x>2
Therefore, the graph represents the function
[tex]y=\begin{cases}x^3-3 & \text{ if } x\le 2 \\ x^2+6 & \text{ if } x>2 \end{cases}[/tex].
