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

How do you determine the domain of a piecewise function?

Back

The domain of a piecewise function is the set of all input values (x-values) for which the function is defined, considering all pieces.

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 do you find the range of a piecewise function?

Back

To find the range, evaluate the output values of each piece of the function and combine them.

Front

What does 'DNE' stand for in function evaluation?

Back

DNE stands for 'Does Not Exist', indicating that the function does not have a value for that input.

Front

What is the notation for an interval that includes its endpoints?

Back

The notation for an interval that includes its endpoints is called a closed interval, denoted by square brackets [a, b].

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What is the notation for an interval that does not include its endpoints?

Back

The notation for an interval that does not include its endpoints is called an open interval, denoted by parentheses (a, 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 input and use the corresponding formula.

Front

What is the significance of the graph of a piecewise function?

Back

The graph of a piecewise function visually represents how the function behaves over different intervals of its domain.

Front

What is a common mistake when working with piecewise functions?

Back

A common mistake is to forget to check which piece of the function applies to a given input value.