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 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 to find the function's value.

Front

What does DNE stand for in the context of functions?

Back

DNE stands for 'Does Not Exist', indicating that a function value cannot be determined for a given input.

Front

If f(x) = { x^2 for x < 0; 2x + 1 for x >= 0, what is f(-2)?

Back

f(-2) = 4.

Front

If f(x) = { x^2 for x < 0; 2x + 1 for x >= 0, what is f(-1)?

Back

f(-1) = -2.

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) 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)) 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 on its respective interval and ensure to indicate open or closed circles at endpoints.

Front

What is the importance of continuity in piecewise functions?

Back

Continuity in piecewise functions ensures that there are no breaks or jumps in the graph, which is important for certain applications.

Front

If m(x) = { 3 for x < -1; x + 2 for x >= -1, what is m(-3)?

Back

m(-3) = 3.