Looking at the function, there are two sections of the graph, one on the interval [-1, 1) and the other on the interval [1, ∞). On the first interval, the function corresponds to a quadratic function. The endpoints are (-1, 1) and (1, 1), so the function should be:
[tex]x^2,-1\leq x<1[/tex]
On the other hand, the second section of the graph is a horizontal parabola, so the function corresponds to a square root function. It passes through the points (1, 1), (4, 2), and (9, 3), so the function should be:
[tex]\sqrt[]{x},1\leq x[/tex]
Then, the piecewise function is:
[tex]f(x)=\begin{cases}x^2,\text{ if }-1\leq x<1 \\ \sqrt[]{x},\text{ if }x\ge1\end{cases}[/tex]
