Calculating Average Rate of Change in Functions

This video lesson by Kirk Wier from emath instruction covers the concept of average rate of change, a key topic in Common Core Algebra 1. The lesson begins with an introduction to the importance of understanding how outputs change relative to inputs. Through various exercises, including a race between Max and Eevee, function analysis, and lemonade sales, the lesson demonstrates how to calculate and interpret the average rate of change. The video also explains the relationship between rate of change and the slope of a line, providing a formula for finding the average rate of change. The lesson concludes with a summary of key points and encourages further practice.

What is the main topic of this lesson?

• Average Rate of Change

• Quadratic Functions

• Linear Equations

• Probability

In the race example, what does M(12) = 30 represent?

• Max's speed after 12 seconds

• Max's distance after 12 seconds

• Eevee's speed after 12 seconds

• Eevee's distance after 12 seconds

How much of a head start does Max give Eevee?

• 20 feet

• 15 feet

• 10 feet

• 25 feet

Does Max catch up to Eevee by the end of the race?

• Yes, they tie

• Yes, he overtakes her

• No, he remains behind

• No, he falls further behind

How far does Max run during the 20-second race?

• 50 feet

• 60 feet

• 35 feet

• 25 feet

What is the average speed of Eevee during the race?

• 1.5 feet per second

• 1.75 feet per second

• 2.0 feet per second

• 2.5 feet per second

The average rate of change is the same as finding the ____ of a line.

• Angle

• Length

• Slope

• Intercept

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

• (a - b) / (f(a) - f(b))

• (f(b) - f(a)) / (b - a)

• (f(a) - f(b)) / (a - b)

• (b - a) / (f(b) - f(a))

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

• 4

• 3

• 2

• 1

If Francis sells 20 glasses of lemonade in 6 hours, what is her average rate of sales?

• 2 glasses per hour

• 3 glasses per hour

• 4 glasses per hour

• 5 glasses per hour