Understanding the Greatest Integer Function

The video tutorial introduces the greatest integer function, also known as the floor function, and explains how to evaluate it for both positive and negative values using a number line. It covers graphing the function, highlighting the pattern of closed and open circles. The tutorial includes practice problems and explores limits involving the greatest integer function, providing a comprehensive understanding of the topic.

What is the greatest integer less than 0.7?

• 0

• 1

• -1

• 0.7

If you plot 1.8 on a number line, which integer is to its left?

• 0

• 2

• 1

• 1.8

How is the greatest integer function graphically represented between 0 and 1?

• A curve from 0 to 1

• A diagonal line from 0 to 1

• A vertical line with a y-value of 1

• A horizontal line with a y-value of 0

What is the greatest integer function of 3.2?

• 2

• 3.2

• 3

• 4

Which integer is the greatest integer less than -3.2?

• -4

• -3.2

• -3

• -2

What is the limit as x approaches 0 from the left of the greatest integer function of x?

• -1

• 1

• Does not exist

• 0

What is the limit as x approaches 2 from the left of the expression greatest integer function of x plus 3x?

• 7

• 8

• 6

• 5

What is the limit as x approaches -3 from the left of 5 minus 2 times the greatest integer function of x?

• 13

• 11

• 15

• 9

What is the limit as x approaches 3 of 2 minus the greatest integer function of negative x?

• Does not exist

• 4

• 5

• 6

What is the greatest integer of positive 2.1 when evaluating the limit as x approaches -2 from the left of the greatest integer function of negative x?

• 2

• 3

• 0

• 1