Piecewise Functions with Domain and Range

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

What does DOMAIN refer to in a function?

Back

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

Front

What does RANGE refer to in 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 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

How do you determine the range of a piecewise function?

Back

To determine the range, evaluate the output values of each piece of the function and combine the results.

Front

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

Back

The range is [3, +∞).

Front

If f(x) = { 2x + 1 for x < 1; x^2 for x ≥ 1 }, what is f(0)?

Back

f(0) = 1.

Front

If f(x) = { -x + 4 for x < 2; 3x for x ≥ 2 }, what is f(3)?

Back

f(3) = 9.

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, +∞).