Understanding the Floor Function

This video tutorial introduces the floor function, also known as the greatest integer function. It explains the function's definition, domain, and range, and demonstrates how to graph it by hand. The tutorial covers different notations for the floor function and compares it with the ceiling function. It provides examples of graphing the floor function, including handling negative values, and offers step-by-step instructions for graphing by hand.

What is the domain of the floor function?

• Integers

• Real numbers

• Natural numbers

• Complex numbers

Which of the following is NOT a common notation for the floor function?

• floor(x)

• ⌊x⌋

• ceil(x)

• int(x)

How does the floor function differ from the ceiling function in terms of notation?

• Floor function uses square brackets, ceiling uses curly brackets

• Floor function uses inward vertical bars at the bottom, ceiling uses them at the top

• Floor function uses parentheses, ceiling uses square brackets

• Floor function uses curly brackets, ceiling uses parentheses

Tags

CCSS.HSF-IF.C.7D

Why is the graph of the floor function discontinuous?

• Because it is a constant function

• Because it is a quadratic function

• Because it is a linear function

• Because it only outputs integers

Tags

CCSS.HSF-IF.C.7D

What is the floor value of 1.9?

• 2

• 1.9

• 1

• 0

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CCSS.HSF.IF.A.2

In the example f(x) = ⌊x + 2⌋, what is the output when x = 1.5?

• 1

• 4

• 3

• 2

Tags

CCSS.HSF-IF.C.7D

What happens to the function value when x reaches an integer in the floor function?

• It decreases

• It remains the same

• It jumps to the next integer

• It becomes zero

Tags

CCSS.HSF-IF.C.7D

What is the floor value of -1.8?

• 0

• -1.8

• -2

• -1

In the example with negative values, what is the output of the floor function when x = -2?

• -1

• -2

• 0

• 1

What is the largest integer less than or equal to 0.5?

• 0.5

• -1

• 1

• 0