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

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

Back

To evaluate a piecewise function at a specific point, determine which piece of the function applies to that point and then use the corresponding expression to find the value.

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, which may vary for different pieces.

Front

What does 'DNE' stand for in the context of functions?

Back

DNE stands for 'Does Not Exist', indicating that a function value is not defined for a particular input.

Front

What is the range of a piecewise function?

Back

The range of a piecewise function is the set of all possible output values (y-values) that the function can produce.

Front

How can you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function according to its defined interval, ensuring to use open or closed circles to indicate whether endpoints are included.

Front

What is the significance of domain restrictions in piecewise functions?

Back

Domain restrictions in piecewise functions indicate the specific intervals where each piece of the function is valid, affecting how the function behaves.

Front

How do you find the value of f(x) when x is in a specific interval?

Back

Identify the interval that contains the value of x, then use the corresponding expression for that interval to calculate f(x).

Front

What is the difference between continuous and discontinuous piecewise functions?

Back

A continuous piecewise function has no breaks or jumps in its graph, while a discontinuous piecewise function has gaps or jumps at certain points.

Front

What is an example of a piecewise function?

Back

An example of a piecewise function is: f(x) = { x^2 for x < 0; 2x + 1 for x ≥ 0 }.