Identifying Functions from Tables

The video tutorial covers identifying different types of functions—linear, quadratic, exponential, and absolute value—using tables without graphing. It emphasizes recognizing patterns, such as common differences for linear functions and second differences for quadratic functions. The tutorial also explains how to identify exponential functions through constant ratios and discusses non-parent functions. The lesson concludes with a final example to reinforce the concepts.

What is the primary basis for all mathematics as discussed in the video?

• Functions

• Equations

• Graphs

• Patterns

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

• Quadratic

• Absolute Value

• Linear

• Exponential

In a quadratic function from a table, what is constant across calculated values?

• Sum of x-values

• First difference

• Second difference

• Ratio of y-values

What indicates a quadratic function when first differences are not constant?

• Constant sum of y-values

• None of the above

• Variable second differences

• Constant second differences

How can you identify a function type if the first difference is not constant?

• None of the above

• Calculate the average of x-values

• Plot the graph

• Check the second difference

What does a constant second difference in a table indicate about the function?

• It is linear

• It is exponential

• It is absolute value

• It is quadratic

What pattern in differences indicates an absolute value function?

• Constant first differences

• None of the above

• Alternating signs in first differences

• Constant second differences

What is a key characteristic of exponential functions identified in the video?

• Constant ratios

• Constant second differences

• All of the above

• Constant first differences

Which function type is identified by a constant ratio of successive y-values?

• Absolute Value

• Linear

• Quadratic

• Exponential

How can the type of a function be deduced from a table without plotting it?

• By analyzing the differences or ratios of y-values

• By determining the maximum y-value

• By finding the median x-value

• By checking the increments in x-values