Piecewise Functions- Alg 2B

A piecewise function is a function that is defined by different expressions or formulas for different intervals of its domain.

The domain of a piecewise function is the set of all possible input values (x-values) for which the function is defined, which may vary across different pieces.

To evaluate a piecewise function at a specific point, determine which interval the point falls into and use the corresponding expression to find the function's value.

The notation f(x) represents the output of the function for a given input x, which may depend on the specific piece of the function applicable to that input.

f(2) = 2^2 = 4.

f(0) = 0^2 = 0.

To graph a piecewise function, plot each piece of the function according to its defined interval, ensuring to use open or closed circles to indicate whether endpoints are included.

f(12) = 4.

f(-2) = 2(-2) + 1 = -4 + 1 = -3.

A piecewise function is continuous if there are no breaks, jumps, or holes in the graph, meaning the function's value approaches the same limit from both sides at the boundaries of the pieces.