Module 14 retake Avg rate of change, intervals, functions

Front

What is the average rate of change of a function?

Back

The average rate of change of a function over an interval is the change in the function's value divided by the change in the input value over that interval.

Front

How do you determine where a function is increasing?

Back

A function is increasing on an interval if the output values (y-values) rise as the input values (x-values) increase.

Front

How do you determine where a function is decreasing?

Back

A function is decreasing on an interval if the output values (y-values) fall as the input values (x-values) increase.

Front

What does it mean for a function to have a positive average rate of change?

Back

A positive average rate of change indicates that the function's output values are increasing over the interval.

Front

What does it mean for a function to have a negative average rate of change?

Back

A negative average rate of change indicates that the function's output values are decreasing over the interval.

Front

How can you find the average rate of change from a graph?

Back

To find the average rate of change from a graph, identify two points on the graph, (x1, y1) and (x2, y2), and use the formula: (y2 - y1) / (x2 - x1).

Front

What is an interval in the context of functions?

Back

An interval is a range of x-values over which a function is analyzed, often expressed in the form (a, b) or [a, b].

Front

What is the significance of critical points in a function?

Back

Critical points are where the function's derivative is zero or undefined, indicating potential local maxima, minima, or points of inflection.

Front

How do you calculate the average rate of change between two specific points?

Back

To calculate the average rate of change between two points (x1, y1) and (x2, y2), use the formula: (y2 - y1) / (x2 - x1).

Front

What is the difference between increasing and decreasing intervals?

Back

Increasing intervals are where the function's output rises, while decreasing intervals are where the function's output falls as x increases.