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 parts of its domain.

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.

Front

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

What is a step function?

Back

A step function is a type of piecewise function that has a graph resembling a series of steps, where the function value remains constant within certain intervals.

Front

How do you find f(x) for a piecewise function?

Back

To find f(x), identify the interval in which x falls and use the corresponding expression for that interval.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, as x increases, the function values (y-values) also increase.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, as x increases, the function values (y-values) decrease.

Front

What is the difference between open and closed intervals?

Back

An open interval does not include its endpoints, while a closed interval includes its endpoints.

Front

How do you determine the intervals of increase and decrease for a piecewise function?

Back

To determine intervals of increase and decrease, analyze the slopes of the function's segments and identify where the function rises or falls.

Front

What is the significance of the endpoints in piecewise functions?

Back

Endpoints determine where the function changes from one expression to another and can affect the continuity of the function.