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.

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

Tags

CCSS.HSF.IF.A.2

Front

What is 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, often specified by the intervals in the piecewise definition.

Front

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 intervals.

Tags

CCSS.HSF-IF.C.7B

Front

How can you graph a piecewise function?

Back

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

Tags

CCSS.HSF-IF.C.7B

Front

What does it mean for a piecewise function to be continuous?

Back

A piecewise function is continuous if there are no breaks, jumps, or holes in the graph at the points where the pieces meet.

Tags

CCSS.HSF-IF.C.7B

Front

What is the significance of endpoints in piecewise functions?

Back

Endpoints in piecewise functions determine whether the function includes or excludes specific values, affecting continuity and the overall graph.

Tags

CCSS.HSF-IF.C.7B

Front

How do you find the value of f(x) for x = -3 in a piecewise function?

Back

To find f(-3), identify the interval that includes -3 and use the corresponding expression to calculate the value.

Tags

CCSS.HSF.IF.A.2

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What is the value of f(-2) if f(x) is defined as 8 for that interval?

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f(-2) = 8, as it falls within the interval where the function is defined as 8.

Tags

CCSS.HSF.IF.A.2

Front

How do you determine f(2) in a piecewise function?

Back

To determine f(2), locate the interval that includes 2 and apply the expression defined for that interval.

Tags

CCSS.HSF.IF.A.2