Understanding Linear Functions from a Table of Values

This video tutorial explains how to determine if a table of values represents a linear function. It covers the concept of rate of change between two points, emphasizing that a linear function has a constant rate of change, known as the slope. The tutorial includes examples to illustrate how to calculate the rate of change and verify linearity both algebraically and graphically. It also demonstrates how to identify non-linear functions and discusses cases with constant outputs.

What is the rate of change in a linear function?

• The product of inputs and outputs

• The difference in inputs divided by the difference in outputs

• The difference in outputs divided by the difference in inputs

• The sum of inputs and outputs

In a linear function, what does a constant rate of change indicate?

• The function is logarithmic

• The function is linear

• The function is exponential

• The function is quadratic

How do you determine if a table represents a linear function?

• By checking if the inputs and outputs are equal

• By checking if the inputs are all positive

• By checking if the rate of change is constant between all pairs of points

• By checking if the outputs are all negative

What is the slope of the function in Example 1?

• -3

• 1

• 0

• 2

In Example 2, why is the table not representing a linear function?

• The inputs are not in order

• The outputs are all the same

• The inputs are negative

• The rates of change are not consistent

What is the rate of change between the first two points in Example 2?

• 3

• 2

• 1

• 1/2

In Example 3, what is the slope of the function?

• 2

• -1

• 0

• 1

Why does the table in Example 3 represent a linear function?

• The inputs are all positive

• The outputs are all the same

• The rate of change is zero

• The inputs and outputs are equal

What does plotting points on a Cartesian plane help verify?

• The function is quadratic

• The function is linear

• The function is exponential

• The function is logarithmic

What indicates a linear function when graphically verified?

• A line passing through all points

• Scattered points

• A circle passing through all points

• A curve passing through all points