Linear and Exponential Functions Analysis

The video tutorial explains how to identify linear functions by examining tables for a constant rate of change. Table A is analyzed and confirmed as a linear function due to its consistent rate of change. In contrast, Table B is identified as an exponential function because its rate of change increases multiplicatively, indicating a growth factor rather than a constant rate.

What is a key characteristic of a linear function?

• It is always decreasing.

• It involves multiplication by a constant factor.

• It has a constant rate of change.

• It has a variable rate of change.

In Table A, what is the rate of change between consecutive outputs?

• Subtract 6

• Add 4

• Add 6

• Multiply by 2

Why is Table A considered a linear function?

• The outputs are subtracted by a constant value.

• The outputs are multiplied by a constant factor.

• The inputs are not evenly spaced.

• The rate of change is constant.

What is the pattern of change in Table B?

• Subtract 10 each time

• Multiply by 2 each time

• Divide by 2 each time

• Add 10 each time

Why is Table B not a linear function?

• The outputs are decreasing.

• The inputs are not evenly spaced.

• The rate of change is not constant.

• The rate of change is constant.

What type of function does Table B represent?

• Exponential

• Quadratic

• Linear

• Logarithmic

Which table represents a linear function?

• Table B

• Both Table A and B

• Table A

• Neither Table A nor B

What is the conclusion about the nature of the functions in the tables?

• Both tables are linear.

• Only Table A is linear.

• Only Table B is linear.

• Neither table is linear.