Piece-wise 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.

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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 then use the corresponding expression to find the value.

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 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 value of f(2) in a piecewise function?

Back

Identify the piece of the function that includes x = 2 and substitute 2 into that expression.

Front

What does DNE mean in the context of functions?

Back

DNE stands for 'Does Not Exist', indicating that a certain value or limit cannot be defined.

Front

What is an interval notation?

Back

Interval notation is a way of representing a range of values using parentheses and brackets, where parentheses indicate that the endpoint is not included and brackets indicate that it is included.

Front

What is the difference between open and closed intervals?

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An open interval does not include its endpoints, while a closed interval includes its endpoints.

Front

How do you express the domain of a function in interval notation?

Back

The domain can be expressed in interval notation by identifying the lowest and highest x-values that the function can take, using brackets or parentheses as appropriate.

Front

What is the significance of the piecewise function's segments?

Back

Each segment of a piecewise function represents a different rule or formula that applies to a specific interval of the domain.