Piecewise Functions

Front

What is a piecewise function?

Back

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

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How do you determine the domain of a piecewise function?

Back

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

Front

What does it mean for a function to behave like a linear function?

Back

Front

What is the significance of domain restrictions in piecewise functions?

Back

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

Front

How can you identify the range of a piecewise function?

Back

The range can be identified by evaluating the output values of each piece of the function over its respective domain.

Front

What is the difference between open and closed intervals?

Back

An open interval (a, b) does not include the endpoints a and b, while a closed interval [a, b] includes both endpoints.

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Back

This notation represents an interval that includes all numbers greater than -1/2 and up to and including 2.

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How do you graph a piecewise function?

Back

To graph a piecewise function, plot each piece on its respective interval and ensure to use open or closed dots based on the interval type.

Front

What is a quadratic function?

Back

Front

How can you tell if a piece of a function is quadratic?

Back

A piece of a function is quadratic if it can be expressed in the form of a quadratic equation and has a parabolic shape when graphed.