Comparing Linear and Nonlinear Functions

In Mr. Wagner's math class, the lesson focuses on understanding linear functions. The video reviews the concept of linear functions, explaining that they form straight lines on graphs and have a constant slope, known as the rate of change. The lesson covers how to identify linear functions from graphs, tables, and equations. It provides examples to illustrate the differences between linear and non-linear functions. The video concludes with a practical example involving the cost of cereal, demonstrating how to write a linear function and interpret its slope.

What shape does the graph of a linear function form?

• A circular line

• A zigzag line

• A curved line

• A straight line

What is another name for the slope of a linear function?

• Quadratic term

• X-intercept

• Y-intercept

• Rate of change

Which of the following graphs represents a linear function?

• A graph with a circular line

• A graph with a straight line

• A graph with a curved line

• A graph with a zigzag line

What indicates a linear function in a table?

• A varying rate of change

• A constant rate of change

• A constant x-value

• A constant y-value

In the table, if the change in y is 3 and the change in x is 3, what is the slope?

• 9

• 0

• 3

• 1

Which equation represents a linear function?

• y = x^3 + 2

• y = x/4 - 3

• y = 3/x - 1/2

• y = x^2 + 1

Why is the equation y = 17 considered a linear function?

• Because it has a constant slope of 1

• Because it represents a horizontal line

• Because it represents a vertical line

• Because it has a variable slope

What is the missing y value that makes the table represent a linear function if x increases by 4 and y increases by 1?

• 3.5

• 4.5

• 2.5

• 1.5

What is the slope of the linear function representing the cost y of x ounces of cereal if the change in y is 1 and the change in x is 4?

• 1/4

• 4

• 1/2

• 1

How would you interpret the slope of 0.25 in the context of the cost of cereal?

• It costs 1 dollar for every ounce

• It costs 1 dollar for every 4 ounces

• It costs 25 cents for every ounce

• It costs 25 cents for every 4 ounces