3.2 Evaluate 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 for different intervals of its domain.

Tags

CCSS.HSF-IF.C.7B

Front

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 then use the corresponding expression to find the function's value.

Tags

CCSS.HSF.IF.A.2

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What does f(0) = -2 indicate in a piecewise function?

Back

It indicates that when the input (x) is 0, the output (f(x)) is -2, based on the definition of the function for that interval.

Tags

CCSS.HSF.IF.A.2

Front

If f(-2) = 4, what does this tell us about the function at x = -2?

Back

It tells us that the output of the function is 4 when the input is -2, indicating the specific value of the function at that point.

Tags

CCSS.HSF.IF.A.2

Front

What is the significance of undefined values in piecewise functions?

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Undefined values indicate that the function does not have a valid output for certain inputs, often due to discontinuities or restrictions in the function's definition.

Tags

CCSS.HSF-IF.C.7B

Front

How can you determine the output of f(1) = 2 in a piecewise function?

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You determine the output by identifying the correct piece of the function that applies when x = 1, which gives the output of 2.

Tags

CCSS.HSF.IF.A.2

Front

What does f(4) = 7 imply about the function's behavior at x = 4?

Back

It implies that the function has a defined value of 7 at x = 4, indicating continuity or a specific output at that point.

Tags

CCSS.HSF.IF.A.2

Front

What does it mean if f(8) = 2 in a piecewise function?

Back

It means that for the input x = 8, the function outputs a value of 2, based on the relevant piece of the function.

Tags

CCSS.HSF.IF.A.2

Front

What is the general form of a piecewise function?

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The general form of a piecewise function is: f(x) = { expression1 for x in interval1, expression2 for x in interval2, ... }.

Front

How do you graph a piecewise function?

Back

To graph a piecewise function, plot each piece according to its defined interval, ensuring to use open or closed circles to indicate whether endpoints are included.

Tags

CCSS.HSF-IF.C.7B