Understanding Linear Functions and Rates

The video tutorial explains how to calculate the average rate of change for the function y = 2x + 5 over the interval from 0 to 3. It begins by defining the average rate of change as the slope or rise over run. The instructor then calculates the Y values for X = 0 and X = 3, resulting in points (0, 5) and (3, 11). Finally, the average rate of change is determined by dividing the change in Y (6) by the change in X (3), resulting in an average rate of change of 2.

What is the average rate of change of a function equivalent to?

• The sum of x-values

• The slope of the function

• The product of y-values

• The difference between x and y

What is the y-value when x is 0 for the function y = 2x + 5?

• 10

• 5

• 2

• 0

What is the y-value when x is 3 for the function y = 2x + 5?

• 6

• 8

• 10

• 11

How do you calculate the change in y?

• Add the initial y-value to the final y-value

• Multiply the initial y-value by the final y-value

• Subtract the initial y-value from the final y-value

• Divide the initial y-value by the final y-value

What is the change in y from 0 to 3 for the function y = 2x + 5?

• 8

• 6

• 3

• 5

What is the change in x from 0 to 3?

• 4

• 1

• 2

• 3

What is the average rate of change over the interval 0 to 3 for the function y = 2x + 5?

• 1

• 2

• 3

• 4

Which of the following best describes the average rate of change?

• The midpoint of the interval

• The total distance covered

• The slope of the line connecting two points

• The sum of all y-values