Question

Which of the following functions is graphed below

Answer 1

darn it i was looking for the same thing 

Answer 2

`y=\begin{cases}x^3-3 & \text{ if } x\le 2 \\ x^2+6 & \text{ if } x>2 \end{cases}`

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
`y=x^3` to three units down.

`y=x^3-3` for x≤2

For x>2, it a the graph of a quadratic function which is generated by shifting the graph of
`y=x^2` to 6 units up.

`y=x^2+6` for x>2

Therefore, the graph represents the function

`y=\begin{cases}x^3-3 & \text{ if } x\le 2 \\ x^2+6 & \text{ if } x>2 \end{cases}`.