Domain & Range, Increasing & Decreasing Intervals

Front

What is the definition of Domain in a function?

Back

The domain of a function is the complete set of possible values of the independent variable (input) for which the function is defined.

Front

What is the definition of Range in a function?

Back

The range of a function is the complete set of possible values of the dependent variable (output) that the function can produce.

Front

How do you determine the domain of a function from its graph?

Back

The domain can be determined by identifying the x-values for which the graph exists. It includes all x-values that the function can take.

Front

How do you determine the range of a function from its graph?

Back

The range can be determined by identifying the y-values that the graph reaches. It includes all y-values that the function can output.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, as the x-values increase, the y-values also increase.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, as the x-values increase, the y-values decrease.

Front

Identify the increasing interval of the function: f(x) = x^2 - 4.

Back

Increasing interval: (2, ∞) and (-∞, -2).

Front

Identify the decreasing interval of the function: f(x) = -x^2 + 4.

Back

Decreasing interval: (-∞, -2) and (2, ∞).

Front

What is the increasing interval for the function f(x) = 3x - 5?

Back

Increasing interval: (-∞, ∞).

Front

What is the decreasing interval for the function f(x) = -2x + 3?

Back

Decreasing interval: (-∞, ∞).