Piecewise Functions

Front

What is a piecewise function?

Back

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

Front

How do you determine the domain of a piecewise function?

Back

The domain of a piecewise function is the union of the domains of each piece, considering the intervals where each piece is defined.

Front

What is interval notation?

Back

Interval notation is a way of writing subsets of the real number line using intervals, such as (a, b) for open intervals and [a, b] for closed intervals.

Front

What does the notation (a, b) mean?

Back

The notation (a, b) represents an open interval, meaning it includes all numbers between a and b, but not a and b themselves.

Front

What does the notation [a, b] mean?

Back

The notation [a, b] represents a closed interval, meaning it includes all numbers between a and b, including a and b.

Front

How do you find the range of a piecewise function?

Back

To find the range, evaluate the outputs of each piece of the function over its domain and combine the results.

Front

What is the significance of the endpoints in interval notation?

Back

Endpoints indicate whether the values at those points are included (closed interval) or excluded (open interval) from the set.

Front

What does DNE stand for in mathematics?

Back

DNE stands for 'Does Not Exist', often used to indicate that a function value is undefined.

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 use the corresponding expression.

Front

What is an increasing interval in a function?

Back

An increasing interval is a range of x-values where the function's output values are rising as x increases.