Average Rate of Change

Front

What is the definition of 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 between two points (x1, y1) and (x2, y2)?

Back

The average rate of change is calculated using the formula: (y2 - y1) / (x2 - x1).

Front

What is the average rate of change of a function f(x) from x = a to x = b?

Back

It is given by the formula: (f(b) - f(a)) / (b - a).

Front

If a climber's altitude changes from 400 feet to 700 feet over 4 hours, how do you find the average rate of change?

Back

Use the formula: (700 - 400) / (6 - 2) = 300 / 4 = 75 feet per hour.

Front

What does a negative average rate of change indicate about a function?

Back

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

Front

What is the average rate of change of the function f(x) = 2x + 3 from x = 1 to x = 5?

Back

The average rate of change is (f(5) - f(1)) / (5 - 1) = (13 - 5) / 4 = 2.

Front

How can you interpret the average rate of change in a real-world context?

Back

It represents the rate at which one quantity changes with respect to another, such as speed, growth rate, or efficiency.

Front

What is the significance of the points (19, -2) and (-11, 10) in calculating average rate of change?

Back

These points provide specific values to apply the average rate of change formula: (-2 - 10) / (19 - (-11)) = -12 / 30 = -2/5.

Front

What is the average rate of change of a linear function?

Back

For a linear function, the average rate of change is constant and equal to the slope of the line.

Front

How do you find the slope of a line given two points?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).