Exploring Linear and Nonlinear Functions

The video tutorial covers linear and nonlinear functions, explaining their differences and how to identify them. It uses examples like a football's trajectory, table data, ticket sales, and the area of a square to illustrate these concepts. Linear functions have a constant rate of change, forming a straight line, while nonlinear functions do not, resulting in curves. The tutorial emphasizes understanding these concepts through real-world examples and data analysis.

What is the main characteristic of a linear function?

• It forms a zigzag pattern.

• It has a variable rate of change.

• It has a constant rate of change.

• It forms a curve.

In the football example, did the football travel the same height each half second?

• It traveled the same height every quarter second.

• It traveled the same height every second.

• No, it did not.

• Yes, it did.

What type of function is represented by the football's height over time?

• Non-linear

• Exponential

• Linear

• Constant

When graphing ordered pairs of time and length, what type of graph is formed?

• A parabolic curve

• A zigzag line

• A straight line

• A curve

What is required for a function to be considered linear?

• A variable rate of change

• A constant rate of change

• A decreasing rate of change

• An increasing rate of change

In the table example, if the x-values increase by 2 and the y-values increase by 18 and 34, what type of function is it?

• Exponential

• Constant

• Linear

• Non-linear

If ticket sales increase by $5 for each ticket sold, what type of function does this represent?

• Linear

• Exponential

• Non-linear

• Quadratic

What is the formula for the area of a square?

• Side length squared

• Side length times 4

• Side length divided by 2

• Side length cubed

Does the area of a square represent a linear or non-linear function?

• Constant

• Linear

• Non-linear

• Exponential

What is the main takeaway from the lesson on linear and non-linear functions?

• Non-linear functions have a constant rate of change.

• Non-linear functions form straight lines.

• Linear functions have a constant rate of change.

• Linear functions have a variable rate of change.