9.4 Features of 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 intervals of its domain.

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CCSS.HSF-IF.C.7B

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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 interval the point falls into and use the corresponding expression to find the function's value.

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CCSS.HSF.IF.A.2

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

How do you find the domain of a piecewise function?

Back

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

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.

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CCSS.HSF-IF.C.7B

Front

What is the significance of the value of f(x) at specific points?

Back

The value of f(x) at specific points indicates the output of the function for those input values, which is crucial for understanding the function's behavior.

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CCSS.8.F.A.1

CCSS.HSF.IF.A.1

Front

How do you determine the output of a piecewise function for a given input?

Back

To determine the output, locate the input in the piecewise function's definition and apply the corresponding formula.

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CCSS.HSF.IF.A.2

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 range of a piecewise function?

Back

To find the range of a piecewise function, evaluate each piece of the function over its domain and combine the resulting output values.

Front

What is the formula for a linear function?

Back

The formula for a linear function is typically expressed as g(x) = mx + b, where m is the slope and b is the y-intercept.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2