Increasing and Decreasing Functions

Front

What is an increasing function?

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 at the first point.

Front

What is a decreasing function?

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 at the first point.

Front

What does it mean for a function to be constant?

Back

A function is constant on an interval if it takes the same value for every point in that interval.

Front

How can you identify intervals of increase on a graph?

Back

Intervals of increase can be identified where the graph rises from left to right.

Front

How can you identify intervals of decrease on a graph?

Back

Intervals of decrease can be identified where the graph falls from left to right.

Front

What is the slope of an increasing function?

Back

The slope of an increasing function is positive.

Front

What is the slope of a decreasing function?

Back

The slope of a decreasing function is negative.

Front

What does a zero slope indicate about a function?

Back

A zero slope indicates that the function is constant over that interval.

Front

What is the significance of critical points in a function's graph?

Back

Critical points are where the function changes from increasing to decreasing or vice versa.

Front

How do you determine if a function is never decreasing?

Back

A function is never decreasing if it is either increasing or constant throughout its domain.