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 the intervals for which each piece of the function is defined and combine them.

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 over its domain and combine the resulting output values.

Front

What does it mean if a function has a domain of (-∞, +∞)?

Back

It means that the function is defined for all real numbers.

Front

What does it mean if a function has a range of [-1, +∞)?

Back

It means that the function outputs values starting from -1 and going up to positive infinity, including -1.

Front

What is an example of a piecewise function?

Back

f(x) = { x^2 for x < 0; 2x + 1 for x ≥ 0 }.

Front

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

Back

The domain is (-∞, +∞).

Front

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

Back

The range is [0, 3].

Front

What is the domain of the function f(x) = { 1/x for x ≠ 0; 0 for x = 0 }?

Back

The domain is (-∞, 0) U (0, +∞).