Question

1. is the graph a piecewise function? why or why not?

rubric

Explanation:

A piecewise function is defined by multiple sub-functions, each applying to a distinct interval of the domain. This graph has two distinct parts: a linear segment for $x \leq 2$ and a curved segment for $x > 2$, with no overlapping $x$-values and each part following a different rule. Additionally, it passes the vertical line test (each $x$-value has exactly one $y$-value), so it is a function made of multiple pieces.

Answer:

Yes, this graph represents a piecewise function. It is composed of two distinct sub-functions that apply to non-overlapping intervals of the $x$-domain, and it satisfies the definition of a function (each input $x$ has exactly one output $y$).