Exploring Rates of Change in Linear and Quadratic Functions

Mr. Kelly introduces the concept of average rate of change, focusing on linear and quadratic functions. He explains how to calculate the rate of change using secant lines and explores the constant rate in linear functions versus the variable rate in quadratic functions. The video also covers how to determine concavity by analyzing changes in the rate of change.

What is the term used to describe the slope of the line that passes through two points on a function?

• Tangent line

• Parallel line

• Normal line

• Secant line

In the context of average rate of change, what does the formula (f(b) - f(a)) / (b - a) represent?

• The change in the independent variable

• The slope of the tangent line

• The change in the dependent variable

• The slope of the secant line

If a linear function passes through the points (0,0) and (3,2), what is the average rate of change?

• 3

• 2/3

• 3/2

• 1/3

For a linear function, if the interval changes but the slope remains the same, what can be said about the average rate of change?

• It varies with the interval

• It remains constant

• It is always zero

• It depends on the function

What is the average rate of change for a linear function that passes through the points (-2, 7) and (-1, 5)?

• -1

• 2

• 1

• -2

Given the quadratic function y = x^2 - 2x, what is the average rate of change from x = 1 to x = 2?

• 1

• 2

• 4

• 3

For the quadratic function y = x^2 - 2x, what is the average rate of change from x = 2 to x = 3?

• 1

• 4

• 2

• 3

How does the average rate of change for a quadratic function change as the interval increases?

• It fluctuates

• It increases

• It decreases

• It remains constant

What is the rate of change of the average rates of change for the quadratic function y = x^2 - 2x?

• 2

• 4

• 1

• 3

If the average rate of change is decreasing over equal length intervals, what can be said about the function?

• It is constant

• It is linear

• It is concave up

• It is concave down