Step Functions and Their Properties

The video tutorial introduces the greatest integer function, also known as the floor function, which rounds down to the nearest integer. It provides examples using both positive and negative numbers to illustrate how the function works. The tutorial then explains how to graph step functions by creating a table of values and plotting points. It also covers transformations of step functions, such as vertical stretching and horizontal compression, and concludes with resources for further learning.

What is another name for the greatest integer function?

• Absolute function

• Ceiling function

• Floor function

• Round function

What does the greatest integer function do to a number like 2.5?

• Rounds it to the nearest integer

• Rounds it down to 2

• Leaves it unchanged

• Rounds it up to 3

If the greatest integer function is applied to 1, what is the result?

• 1.5

• 1

• 0

• 2

How does the greatest integer function handle negative numbers like -4.5?

• Rounds it to the nearest integer

• Leaves it unchanged

• Rounds it up to -4

• Rounds it down to -5

On a number line, which direction does the greatest integer function round negative numbers?

• To the right

• To the left

• Upwards

• Downwards

What is the first step in graphing a step function?

• Drawing the graph

• Calculating the range

• Creating a table of values

• Finding the domain

What does an open circle on a step function graph indicate?

• The function value is not included

• The graph is linear

• The function value is included

• The graph is continuous

Why is the step function considered a function?

• It passes the horizontal line test

• It passes the vertical line test

• It is a linear function

• It is a quadratic function

What effect does multiplying the step function by 2 have on the graph?

• Vertical stretch

• Horizontal compression

• Vertical compression

• Horizontal stretch

What happens when the step function is grouped with the x variable?

• It causes a vertical stretch

• It causes a horizontal stretch

• It causes a horizontal compression

• It causes a vertical compression