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 determine the value of a piecewise function at a specific point?

Back

To determine the value of a piecewise function at a specific point, identify which interval the point falls into and use the corresponding expression.

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 a specific interval.

Front

What is the domain of a piecewise function?

Back

The domain of a piecewise function is the set of all possible 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 (f(x)-values) that the function can produce.

Front

How do you find the number of pieces in a piecewise function?

Back

Count the number of distinct expressions or segments defined for different intervals in the function.

Front

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

Back

Endpoints determine whether the function includes or excludes certain values, affecting the continuity and behavior of the function.

Front

What is a common notation used for piecewise functions?

Back

Piecewise functions are often written using curly braces, with each piece defined for its corresponding interval.

Front

How do you evaluate a piecewise function at a boundary point?

Back

Evaluate the function using the expression defined for the interval that includes the boundary point.

Front

What is the difference between open and closed intervals in piecewise functions?

Back

Open intervals do not include endpoints (e.g., (a, b)), while closed intervals do include endpoints (e.g., [a, b]).