graphing 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?

Back

To evaluate a piecewise function, identify the interval in which the input value falls and use the corresponding expression to find the output.

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 for which the function is defined, often represented as intervals.

Front

What is the range of a piecewise function?

Back

The range of a piecewise function is the set of all possible output values that the function can produce.

Tags

CCSS.HSF-IF.C.7B

Front

How do 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 dots as appropriate.

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 a jump discontinuity in a piecewise function?

Back

A jump discontinuity occurs when the left-hand limit and right-hand limit at a point do not equal each other, causing a 'jump' in the graph.

Tags

CCSS.8.F.A.3

Front

How can you determine the number of pieces in a piecewise function?

Back

The number of pieces in a piecewise function is determined by the number of different expressions or formulas used to define the function.

Tags

CCSS.HSF-IF.C.7B

Front

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

Back

Endpoints indicate where one piece of the function ends and another begins, and they can be included or excluded from the domain.

Tags

CCSS.HSF-IF.C.7B

Front

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

Back

To find f(x), substitute the given x value into the appropriate piece of the function based on its defined intervals.

Tags

CCSS.HSF.IF.A.2