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 domain of a piecewise function?

Back

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

Front

What does the notation (-∞, +∞) represent?

Back

It represents the entire set of real numbers, indicating that the function is defined for all x values.

Front

What is the domain restriction for the function defined as f(x) = { x^2 for x < 0, 2x for x ≥ 0 }?

Back

The domain is (-∞, 0) U [0, +∞).

Front

What does the notation [a, b] mean in terms of domain?

Back

It means that the interval includes both endpoints a and b, indicating that a and b are part of the domain.

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

How can you graph a piecewise function?

Back

To graph a piecewise function, plot each piece on its respective interval and ensure that the transitions between pieces are clear.

Front

What is the domain of the function f(x) = { 3 for x < 1, x + 2 for x ≥ 1 }?

Back

The domain is (-∞, 1) U [1, +∞).

Front

What does the notation U represent in interval notation?

Back

The notation U represents the union of two sets, combining their elements.

Front

How do you find the range of a piecewise function?

Back

To find the range, evaluate the outputs of each piece of the function over its domain and combine the results.