Increasing and Decreasing Intervals & Domain and Range

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 based on its domain.

Front

What does it mean for a function to be increasing on an interval?

Back

A function is increasing on an interval if, for any two points in that interval, the function's value at the second point is greater than the value at the first point.

Front

What does it mean for a function to be decreasing on an interval?

Back

A function is decreasing on an interval if, for any two points in that interval, the function's value at the second point is less than the value at the first point.

Front

What is interval notation?

Back

Interval notation is a way of writing subsets of the real number line using parentheses and brackets to indicate whether endpoints are included or excluded.

Front

What do parentheses ( ) indicate in interval notation?

Back

Parentheses indicate that the endpoint is not included in the interval.

Front

What do square brackets [ ] indicate in interval notation?

Back

Square brackets indicate that the endpoint is included in the interval.

Front

How do you express the domain of 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 is the domain of the function f(x) = 1/x?

Back

The domain is all real numbers except x = 0, expressed in interval notation as (-∞, 0) ∪ (0, ∞).

Front

What is the increasing interval for the function f(x) = x^2 on the graph?

Back

The increasing interval is (0, ∞).

Front

What is the decreasing interval for the function f(x) = -x^2 on the graph?

Back

The decreasing interval is (-∞, 0).