8.6.5 HOMEWORK - Increasing and Decreasing Functions

Front

What is an increasing function?

Back

A function is increasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2 then f(x1) < f(x2).

Front

What is a decreasing function?

Back

A function is decreasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2 then f(x1) > f(x2).

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 do you identify increasing intervals on a graph?

Back

Increasing intervals can be identified by looking for sections of the graph where the y-values rise as you move from left to right.

Front

How do you identify decreasing intervals on a graph?

Back

Decreasing intervals can be identified by looking for sections of the graph where the y-values fall as you move from left to right.

Front

What is the notation for an interval?

Back

Intervals are often expressed in interval notation, such as (a, b) for open intervals or [a, b] for closed intervals.

Front

What is the difference between open and closed intervals?

Back

An open interval (a, b) does not include the endpoints a and b, while a closed interval [a, b] includes both endpoints.

Front

How can you determine if a function is increasing or decreasing from its derivative?

Back

If the derivative of a function is positive on an interval, the function is increasing; if the derivative is negative, the function is decreasing.

Front

What is a critical point in the context of increasing and decreasing functions?

Back

A critical point is where the derivative is zero or undefined, which may indicate a change in the increasing or decreasing behavior of the function.

Front

What is the significance of the y-axis in determining function behavior?

Back

The y-axis represents the output values of the function, which helps in identifying whether the function is increasing or decreasing.