11.19.24 Average rate of change

Front

What is the average rate of change?

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 calculate the average rate of change from 20 to 40 minutes?

Back

Average rate of change = (Change in value) / (Change in time) = (Value at 40 minutes - Value at 20 minutes) / (40 - 20).

Front

What does a negative average rate of change indicate?

Back

A negative average rate of change indicates that the function is decreasing over the interval.

Front

In the equation y = mx + b, what does 'm' represent?

Back

'm' represents the slope of the line, which is the rate of change.

Front

What is the slope of the line in the equation y = 7 - 14x?

Back

The slope is -14, indicating a decrease of 14 units in y for every 1 unit increase in x.

Front

How do you interpret the rate of change from a graph?

Back

The rate of change can be interpreted as the slope of the line connecting two points on the graph.

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

If a graph shows a constant rate of change, what does that imply?

Back

It implies that the relationship between the variables is linear.

Front

What is the average rate of change from x=0 to x=1 if the function value changes from 0 to 3?

Back

Average rate of change = (3 - 0) / (1 - 0) = 3.

Front

What does a slope of 0 indicate about a function?

Back

A slope of 0 indicates that the function is constant over that interval.