Piecewise Functions

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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.

Tags

CCSS.HSF-IF.C.7B

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How do you determine the domain of a piecewise function?

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The domain of a piecewise function is the union of the domains of each piece, considering the intervals where each piece is defined.

Front

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

Back

Tags

CCSS.8.F.A.3

Front

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

Back

Front

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

Back

Breakpoints are the values in the domain where the function changes from one expression to another, affecting the function's behavior.

Tags

CCSS.HSF-IF.C.7B

Front

How can you graph a piecewise function?

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To graph a piecewise function, plot each piece of the function over its specified interval and ensure to indicate open or closed circles at breakpoints.

Tags

CCSS.HSF-IF.C.7B

Front

What is the notation used for piecewise functions?

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Piecewise functions are often written using braces, for example: @@f(x) = \begin{cases} x^2 & \text{if } x < 0 \\ 2x + 1 & \text{if } x \geq 0 \end{cases}@@.

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What is the range of a piecewise function?

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The range of a piecewise function is the set of all possible output values (y-values) that the function can produce, based on its defined pieces.

Tags

CCSS.HSF-IF.C.7B

Front

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

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To evaluate a piecewise function at a specific point, determine which interval the point falls into and use the corresponding expression to find the output.

Tags

CCSS.HSF.IF.A.2

Front

What is an example of a piecewise function?

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An example of a piecewise function is: @@f(x) = \begin{cases} x + 2 & \text{if } x < 1 \\ 3 & \text{if } x = 1 \\ x^2 & \text{if } x > 1 \end{cases}@@.