piecewise functions

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

What does the domain of a function represent?

Back

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

Front

How do you determine the domain of a piecewise function?

Back

To determine the domain of a piecewise function, identify the intervals for which each piece of the function is defined and combine them.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

How can you find the value of a piecewise function at a specific point?

Back

To find the value of a piecewise function at a specific point, determine which piece of the function applies to that input value and evaluate it.

Front

What is the significance of the endpoints in a piecewise function?

Back

Endpoints in a piecewise function indicate where one piece of the function ends and another begins, and they can be included or excluded from the domain.

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, meaning it can be drawn without lifting the pencil.

Front

What is a discontinuity in a piecewise function?

Back

A discontinuity in a piecewise function occurs when there is a break or jump in the function's graph, often at the endpoints of the pieces.

Front

How do you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function on its respective interval, paying attention to whether endpoints are included or excluded.

Front

What is the difference between open and closed intervals?

Back

An open interval does not include its endpoints (e.g., (a, b)), while a closed interval includes its endpoints (e.g., [a, b]).