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 express the domain of a piecewise function in interval notation?

Back

The domain of a piecewise function can be expressed in interval notation by combining the intervals for which the function is defined, using parentheses for open intervals and brackets for closed intervals.

Front

What does the notation f(x) mean in a piecewise function?

Back

f(x) represents the output of the function for a given input x, where the specific expression used depends on the interval in which x falls.

Front

How do you determine the value of f(x) for a piecewise function?

Back

To determine f(x), identify the interval that contains the input x and use the corresponding expression for that interval.

Front

What is the significance of the endpoints in interval notation?

Back

Endpoints indicate whether the interval includes or excludes the boundary values; brackets [ ] include the endpoint, while parentheses ( ) exclude it.

Front

What is the domain of the function f(x) = { x^2 for x < 0; 2x for x >= 0 }?

Back

The domain is (-∞, ∞) because the function is defined for all real numbers.

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.

Front

What is the range of the function f(x) = { x^2 for x < 0; 2x for x >= 0 }?

Back

The range is [0, ∞) because x^2 produces non-negative values and 2x also produces non-negative values for x >= 0.

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 do you graph a piecewise function?

Back

To graph a piecewise function, plot each piece on its respective interval, ensuring to use open or closed dots at the endpoints based on the interval notation.