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

To determine the domain, identify all the intervals for which the function is defined and combine them.

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

How do you find the range of a piecewise function?

Back

Evaluate each piece of the function over its interval and combine the resulting output values.

Front

What does DNE stand for in the context of functions?

Back

DNE stands for 'Does Not Exist', indicating that a certain value is not in the function's output.

Front

What is the difference between open and closed intervals?

Back

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

Front

What is the notation for the union of two sets?

Back

The notation for the union of two sets is 'U', which combines all elements from both sets without duplication.

Front

How can you express the domain of a function using interval notation?

Back

The domain can be expressed using interval notation, which uses parentheses for open intervals and brackets for closed intervals.

Front

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

Back

Endpoints determine whether the function includes or excludes certain values in its domain and range.

Front

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

Back

To evaluate, identify which piece of the function corresponds to the input value and apply that piece's formula.