Alg 2. Domain and Range of Piecewise functions.

Front

What is the definition of 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 all the input values (x-values) for which the function is defined, considering the conditions for each piece.

Front

What is the definition of the range of a function?

Back

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

Front

How do you find the range of a piecewise function?

Back

To find the range, evaluate each piece of the function to determine the output values and combine them to form the overall range.

Front

What does the notation (-∞, 3] represent?

Back

The notation (-∞, 3] represents all real numbers less than or equal to 3.

Front

What does the notation [-4, 5] represent?

Back

The notation [-4, 5] represents all real numbers from -4 to 5, including -4 and 5.

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 include their endpoints (e.g., [a, b]).

Front

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

Back

The domain is (-∞, 1) U [1, +∞).

Front

What is the range of the function f(x) = { x^2 for x < 1; 3 for x >= 1 }?

Back

The range is [0, 3].

Front

How do you express the domain of a function that is defined for all real numbers except x = 0?

Back

The domain can be expressed as (-∞, 0) U (0, +∞).