Distinguishing Linear and Exponential Functions Using Function Tables

This lesson teaches how to distinguish between linear and exponential functions by examining function tables. Linear functions show equal differences between outputs, while exponential functions show equal factors. The video addresses common misunderstandings, such as the meaning of equal intervals and the correct use of exponents. It provides examples of identifying both linear and exponential functions, including cases with decreasing outputs and negative numbers.

What is the main characteristic of a linear function?

• It multiplies by a constant factor each time.

• It has equal differences over equal intervals.

• It decreases exponentially.

• It has a constant factor.

When constructing a function table, what is a common misunderstanding about the exponent in exponential functions?

• The exponent should be divided by the base each time.

• The exponent should be added each time.

• The exponent should be multiplied by the base each time.

• The exponent should be subtracted each time.

What is the relationship between the x values in a function table for both linear and exponential functions?

• They must increase by different amounts each time.

• They must increase by the same amount each time.

• They must decrease by the same amount each time.

• They must remain constant.

How can you identify an exponential function from a function table?

• By finding a constant sum in the output values.

• By finding a constant subtraction in the output values.

• By finding a constant factor that multiplies the output values.

• By finding equal differences in the output values.

What pattern is observed in a function table that represents an exponential function with a decreasing sequence?

• The output values are added by a constant number.

• The output values are multiplied by a constant factor.

• The output values are divided by a constant factor.

• The output values are subtracted by a constant number.

In a function table with negative numbers, what indicates a linear function?

• A constant sum between outputs.

• A constant difference between outputs.

• A constant division between outputs.

• A constant factor between outputs.

What does a sketch of a graph from a linear function table typically look like?

• A curve that increases rapidly.

• A curve that decreases rapidly.

• A zigzag pattern.

• A straight line.