intervals of increase/decrease

Front

What is an interval of increase?

Back

An interval of increase is a range of x-values over which the function's output (y-values) is rising as x increases.

Front

What is an interval of decrease?

Back

An interval of decrease is a range of x-values over which the function's output (y-values) is falling as x increases.

Front

How do you determine intervals of increase or decrease from a graph?

Back

To determine intervals of increase or decrease from a graph, observe the slope of the graph: if the graph rises, it's increasing; if it falls, it's decreasing.

Front

What does it mean for a function to be a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

Front

What is 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

What is 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 notation for an interval?

Back

Intervals are often expressed in parentheses or brackets, e.g., (a, b) for open intervals and [a, b] for closed intervals.

Front

What does the notation (a, b) represent?

Back

The notation (a, b) represents an open interval that includes all numbers between a and b, but not a and b themselves.

Front

What does the notation [a, b] represent?

Back

The notation [a, b] represents a closed interval that includes all numbers between a and b, including a and b.

Front

How can you identify a function from a set of ordered pairs?

Back

A set of ordered pairs is a function if no two pairs have the same first element (x-value).