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?

Back

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

Front

What does the graph of a piecewise function look like?

Back

The graph of a piecewise function consists of multiple segments, each representing a different expression for specific intervals.

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.

Front

What is the range of a piecewise function?

Back

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

Front

What does it mean for a function to be continuous?

Back

A function is continuous if there are no breaks, jumps, or holes in its graph.

Front

What is a discontinuity in a piecewise function?

Back

A discontinuity occurs when there is a break in the graph of the function, often at the points where the pieces meet.

Front

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

Back

You can determine if a piecewise function is increasing or decreasing by analyzing the slopes of the segments in its graph.

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.

Front

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

Back

To find the value at a specific point, substitute the point into the appropriate piece of the function based on its interval.