Evaluate Piecewise Functions #1 & #2

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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

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

Tags

CCSS.HSF.IF.A.2

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What does it mean for a function to be undefined at a point?

Back

A function is undefined at a point if there is no valid output for that input, often due to division by zero or if the input does not fall within the function's defined intervals.

Tags

CCSS.HSF.IF.A.1

CCSS.8.F.A.1

Front

What is the significance of 'No Real Number Solution' in the context of piecewise functions?

Back

'No Real Number Solution' indicates that there is no value in the real number system that satisfies the function for the given input.

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How can you determine if a piecewise function is continuous at a point?

Back

A piecewise function is continuous at a point if the limit from the left equals the limit from the right and both equal the function's value at that point.

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What is the difference between a function being undefined and having a value of zero?

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A function being undefined means there is no output for that input, while a value of zero means the function outputs zero for that input.

Tags

CCSS.HSF.IF.A.2

Front

What is the importance of domain in piecewise functions?

Back

The domain of a piecewise function defines the set of input values for which the function is defined, and it can vary across different pieces of the function.

Tags

CCSS.HSF-IF.C.7B

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

Front

What is an example of a piecewise function?

Back

An example of a piecewise function is: f(x) = { x^2 for x < 0; 2x + 1 for x >= 0 }.

Front

What does it mean for a function to have multiple outputs for a single input?

Back

A function cannot have multiple outputs for a single input; if it does, it is not a function. Piecewise functions may have different expressions for different intervals but only one output for each input.

Tags

CCSS.8.F.A.1