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 range of a piecewise function?

Back

To determine the range, evaluate the function at the endpoints of each interval and identify the output values.

Front

What does the notation [-3] U [0] U [3] represent?

Back

This notation represents the union of sets, indicating that the range includes -3, 0, and 3 as distinct values.

Front

What is the significance of intervals in piecewise functions?

Back

Intervals indicate the specific domains over which different expressions of the function apply.

Front

How do you find the interval of increase for a piecewise function?

Back

To find the interval of increase, analyze the function's derivative or evaluate the function's values over its domain.

Front

What does DNE stand for in the context of functions?

Back

DNE stands for 'Does Not Exist', indicating that a function value is undefined for a given input.

Front

How can you evaluate f(-2) in a piecewise function?

Back

To evaluate f(-2), identify which piece of the function applies to the input -2 and calculate the output.

Front

What is the difference between closed and open intervals?

Back

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

Front

What is the domain of a piecewise function?

Back

The domain of a piecewise function is the set of all possible input values for which the function is defined.

Front

How do you graph a piecewise function?

Back

To graph a piecewise function, plot each piece according to its defined interval and connect the points appropriately.