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.

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 for that interval.

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, which may vary across different pieces.

Front

What does the notation f(x) mean in the context of piecewise functions?

Back

In piecewise functions, f(x) represents the output value of the function for a given input x, determined by the specific piece of the function that applies to that x.

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.

Front

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

Back

Endpoints in a piecewise function indicate the boundaries of the intervals; whether they are included or excluded affects the function's continuity.

Front

How do you find the value of a piecewise function at a boundary point?

Back

To find the value of a piecewise function at a boundary point, check both pieces of the function to see if the boundary point is included in either piece.

Front

What is the range of a piecewise function?

Back

The range of a piecewise function is the set of all output values (y-values) that the function can produce, which may vary across different pieces.

Front

What is the difference between a continuous and a discontinuous piecewise function?

Back

A continuous piecewise function has no breaks or jumps in its graph, while a discontinuous piecewise function has breaks or jumps at certain points.

Front

How do you determine if a piecewise function is increasing or decreasing?

Back

To determine if a piecewise function is increasing or decreasing, analyze the slopes of the pieces over their respective intervals.