Understanding Linear Functions and Tables

The video tutorial explains the difference between linear and nonlinear functions, focusing on how to identify them using tables of values. It covers the concept of constant rate of change and how to determine linearity by analyzing changes in output and input values. The tutorial provides examples of both linear and nonlinear functions, including cases with negative values, and offers practical tips for students to apply in their assignments.

What is a key characteristic of a linear function?

• It cannot be represented on a graph.

• It has a constant rate of change.

• It forms a curved line on a graph.

• It has a variable rate of change.

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

• By counting the number of data points.

• By ensuring the change in Y over change in X is constant.

• By checking if the graph is a circle.

• By checking if the table has more than five entries.

What indicates a nonlinear function in a table of values?

• The table has only negative values.

• The changes in Y over changes in X are not constant.

• The table has only positive values.

• All changes in Y are the same.

In a table, if the input values increase by one, what should you check to determine linearity?

• The consistency of changes in output values.

• The number of input values.

• The difference between the first and last output values.

• The sum of all output values.

What is the result if the ratio of change in Y over change in X is consistent across a table?

• The function is nonlinear.

• The function is undefined.

• The function is quadratic.

• The function is linear.

What should you do if the input values in a table do not increase by one?

• Assume the function is nonlinear.

• Ignore the table.

• Check the change in Y over change in X.

• Only look at the first and last values.

If a table's output values are -8, -16, -24, and -32, what can be inferred?

• The function is linear.

• The function is undefined.

• The function is nonlinear.

• The function is exponential.

What is a common mistake when determining linearity from a table?

• Assuming all tables are linear.

• Not calculating the ratio of changes.

• Ignoring the input values.

• Not checking the graph.

Why is it important to check the ratio of changes in a table?

• To confirm the function's linearity.

• To identify the minimum value.

• To determine the number of data points.

• To find the maximum value.

What does a consistent change in output over input indicate?

• A nonlinear function.

• A linear function.

• A quadratic function.

• An undefined function.