Question

Write the equation of the piece wise function that is represented by the graph.

Answer 1

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:

`x^2,-1\leq x<1`

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:

`\sqrt[]{x},1\leq x`

Then, the piecewise function is:

`f(x)=\begin{cases}x^2,\text{ if }-1\leq x<1 \\ \sqrt[]{x},\text{ if }x\ge1\end{cases}`