IM2: Piecewise Functions 2023

Front

What is a piecewise function?

Back

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

Front

How do you determine if a relation is a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value).

Front

What are domain restrictions in piecewise functions?

Back

Domain restrictions specify the values of x for which each piece of the function is valid.

Front

Back

It means that x is greater than a and less than or equal to b.

Front

How do you evaluate a piecewise function at a specific point?

Back

To evaluate a piecewise function at a specific point, determine which piece of the function applies to that point and use the corresponding formula.

Front

What is the significance of the endpoints in piecewise functions?

Back

Endpoints indicate where one piece of the function ends and another begins, and they can be included or excluded based on the inequality used.

Front

How many pieces can a piecewise function have?

Back

A piecewise function can have any number of pieces, depending on how it is defined.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What does it mean for a function to be continuous?

Back

A function is continuous if there are no breaks, jumps, or holes in its graph.

Front

How do you graph a piecewise function?

Back

To graph a piecewise function, plot each piece according to its domain restrictions and connect them appropriately.