Greatest Integer Function Concepts

The video tutorial introduces the greatest integer function, also known as the step function. It defines the function as the greatest integer less than or equal to a given real number. Through examples, the video illustrates how the function works for both positive and negative numbers, as well as integers and non-integers. The behavior of the function is generalized, and its graph is plotted to show its step-like appearance. The tutorial concludes by discussing the domain and range of the function, highlighting that the domain is all real numbers and the range is all integers.

What is the greatest integer function also known as?

• Linear function

• Exponential function

• Step function

• Quadratic function

If x is 2.7, what is the greatest integer less than or equal to x?

• 3

• 2.7

• 1

• 2

For x = -3.2, what is the greatest integer less than x?

• -2

• -3

• -4

• -5

What is the value of the greatest integer function for x = 0.75?

• -1

• 1

• 0.75

• 0

What is the value of the greatest integer function for x = 5?

• 5.5

• 5

• 4

• 6

What is the value of the greatest integer function for x in the interval [0, 1)?

• 1

• x

• -1

• 0

In the interval [1, 2), what is the value of the greatest integer function?

• 2

• 1

• 0

• 3

How does the graph of the greatest integer function appear?

• Step-like

• Parabolic

• Circular

• Linear

What is the domain of the greatest integer function?

• All integers

• All real numbers

• Positive integers

• Negative integers

What is the range of the greatest integer function?

• Negative real numbers

• Positive real numbers

• All integers

• All real numbers