Quick Flashcard - Piecewise Defined Functions

Front

What is a piecewise-defined function?

Back

A piecewise-defined function is a function that is defined by different expressions or formulas for different intervals of its domain.

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

Back

To evaluate a piecewise-defined 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

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.

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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 do you find the domain of a piecewise-defined function?

Back

To find the domain of a piecewise-defined 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?

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A function is continuous if there are no breaks, jumps, or holes in its graph, meaning it can be drawn without lifting the pencil.

Tags

CCSS.HSF-IF.C.7B

Front

What is the significance of the endpoints in a piecewise-defined function?

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Endpoints in a piecewise-defined function indicate where the function changes from one expression to another, and they can be included or excluded from the domain.

Tags

CCSS.HSF-IF.C.7B

Front

How do you graph a piecewise-defined function?

Back

To graph a piecewise-defined function, plot each piece of the function on its respective interval, ensuring to use open or closed circles at endpoints based on inclusion.

Tags

CCSS.HSF-IF.C.7B

Front

What is a common application of piecewise-defined functions in real life?

Back

Piecewise-defined functions are commonly used to model situations with different rates or conditions, such as tax brackets, utility rates, or salary structures.

Front

What is the formula for Lea's weekly pay based on hours worked?

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Lea's weekly pay can be represented as: P(h) = 7h for 0 ≤ h ≤ 40, and P(h) = 10.5h - 140 for h > 40.