Analyzing Differences in Functions

The video tutorial explains how to determine if a function represented in a table is linear, quadratic, or neither. It uses three examples to illustrate the process: identifying a linear function by constant first differences, a quadratic function by constant second differences, and a function that is neither. The tutorial emphasizes the importance of analyzing differences between table values to classify the function type.

What is the primary goal when analyzing tables in this lesson?

• To identify the type of function represented

• To calculate the sum of all values

• To find the maximum value in the table

• To determine the average of the values

Which type of function is identified by a constant first difference?

• Cubic

• Linear

• Exponential

• Quadratic

In Table A, what is the constant difference between consecutive y-values?

• 5

• 4

• 3

• 2

What does a constant first difference in a table indicate?

• The function is neither linear nor quadratic

• The function is exponential

• The function is linear

• The function is quadratic

In Table B, what is the first difference between the y-values from 4 to 5?

• 3

• 4

• 2

• 1

What pattern in the second difference indicates a quadratic function?

• The second difference is constant

• The second difference is increasing

• The second difference is zero

• The second difference is decreasing

In Table B, what is the second difference between the first differences from 1 to 3?

• 1

• 2

• 3

• 4

What type of function is Table B representing?

• Cubic

• Linear

• Quadratic

• Exponential

In Table C, what is the first difference between the y-values from 4 to 5?

• 3

• 2

• 4

• 1

What does a changing second difference in a table indicate?

• The function is linear

• The function is exponential

• The function is quadratic

• The function is neither linear nor quadratic