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 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 piece of the function applies to that point based on its domain.

Front

What does the domain of a piecewise function represent?

Back

The domain of a piecewise function represents the set of input values (x-values) for which the function is defined.

Front

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

Back

Endpoints indicate whether the function includes or excludes certain values in its domain, affecting continuity and limits.

Front

How do you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function according to its defined domain, ensuring to use open or closed circles at endpoints as needed.

Front

What is the value of f(0) if f(x) = { 2x + 2 for x < 0; 4 for x ≥ 0 }?

Back

4

Front

What is the domain restriction of the function f(x) = { x^2 for x < 0; 3x - 1 for x ≥ 0 }?

Back

x ≥ 0 for the second piece.

Front

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

Back

DNE stands for 'Does Not Exist', indicating that the function does not have a value at that point.

Front

Using the graph of a piecewise function, how do you find f(-3)?

Back

Locate -3 on the x-axis, determine which piece of the function applies, and read the corresponding y-value.

Front

What is the value of f(-2) if f(x) = { 4 for x < 0; x + 2 for x ≥ 0 }?

Back

4