Comparing Linear and Nonlinear Functions

This video tutorial covers the topic of comparing linear and non-linear functions. It begins with an introduction to the essential question and required materials. The video explains how to identify linear functions by their constant rate of change and slope, and how to recognize non-linear functions using tables and visual cues. It also covers classifying equations as linear or non-linear based on their form and components. The tutorial concludes with practice problems and a summary of key points.

What is the key characteristic of a non-linear function?

• It has a constant rate of change.

• It can be represented by y = mx + b.

• Its graph is a straight line.

• It does not have a constant rate of change.

How do you determine the slope from a table of values?

• By adding the x-values and y-values together.

• By looking at the change in x-values only.

• By looking at the change in y-values only.

• By dividing the change in y-values by the change in x-values.

What does it mean if the changes in y-values are not constant in a table?

• The function is undefined.

• The function has a constant rate of change.

• The function is non-linear.

• The function is linear.

How can you visually identify a non-linear function on a graph?

• The graph is a straight line.

• The graph is a vertical line.

• The graph is not a straight line.

• The graph is horizontal.

Why can't vertical lines be considered functions?

• Because they have a constant rate of change.

• Because they do not pass the vertical line test.

• Because they are non-linear.

• Because they are horizontal.

Which form represents a linear equation?

• y = 1/x

• y = ax^2 + bx + c

• y = mx + b

• y = x^3

What indicates that an equation is non-linear?

• It has a constant rate of change.

• It can be graphed as a straight line.

• It has exponents or variables in the denominator.

• It follows the form y = mx + b.

What does the caret symbol (^) represent in equations?

• Addition

• Subtraction

• Exponentiation

• Division

Which of the following is a non-linear equation?

• y = 6x - 3

• y = 2x + 5

• y = 4/x

• y = 4x + 7

Why is the equation y = 4/x considered non-linear?

• Because it has a constant rate of change.

• Because it can be graphed as a straight line.

• Because it follows the form y = mx + b.

• Because it has a variable in the denominator.