Understanding Linear Functions and Rate of Change

The video tutorial explains how to determine if tables represent linear functions by calculating the rate of change, which should be constant. It demonstrates this process through three tables, showing calculations of the rate of change and identifying which tables represent linear functions based on consistent slopes.

What is a key characteristic of a linear function?

• Constant rate of change

• Variable rate of change

• No rate of change

• Increasing rate of change

How do you find the rate of change in a table?

• By multiplying the function values

• By dividing the change in function values by the change in X values

• By subtracting the X values

• By adding the function values

What is the rate of change between the points (0, 1) and (2, 7)?

• 2

• 5

• 4

• 3

Why does the first table not represent a linear function?

• The function values are the same

• The rate of change is not constant

• The X values are the same

• The rate of change is constant

What is the rate of change for the second table?

• -1

• -2

• -3

• -4

What does a constant rate of change indicate about a table?

• It represents a logarithmic function

• It represents an exponential function

• It represents a linear function

• It represents a quadratic function

What is the rate of change for the third table?

• 1/5

• 1/2

• 1/3

• 1/4

Which tables represent linear functions?

• None

• First and third

• Second and third

• First and second

What is the slope between the points (3, 2) and (6, 3) in the third table?

• 1/2

• 1/3

• 1/4

• 1/5

What does a slope of 1/3 indicate about the third table?

• It has a variable rate of change

• It has a constant rate of change

• It is not a linear function

• It is a quadratic function