Understanding Limits and the Greatest Integer Function

The video tutorial explains the greatest integer function, also known as the floor function, and how to express it using different notations. It demonstrates how to graph the function using a graphing calculator, highlighting its discontinuities and endpoints. The tutorial then focuses on calculating one-sided and regular limits of the function, both graphically and numerically, using the calculator's table feature to verify the results. The video concludes by emphasizing the importance of understanding the behavior of the function as it approaches specific values.

What does the function f(x) = greatest integer of (2 - x) represent?

• The average of 2 and x

• The exact value of 2 - x

• The smallest integer greater than or equal to 2 - x

• The largest integer less than or equal to 2 - x

Which tool is used to graphically analyze the function f(x) = greatest integer of (2 - x)?

• A statistical software

• A spreadsheet software

• A scientific calculator

• A graphing calculator

What is the behavior of the function at x = 0?

• The function value is 1

• The function value is 2

• The function value is 0

• The function value is -1

What is the limit of f(x) as x approaches 3 from the right?

• 0

• 1

• -2

• -1

What is the limit of f(x) as x approaches 3 from the left?

• -1

• 0

• -2

• 1

Why does the limit of f(x) as x approaches 3 not exist?

• The function is undefined at x = 3

• The one-sided limits are not equal

• The one-sided limits are equal

• The function is continuous at x = 3

What feature of the graphing calculator is used to verify limits numerically?

• The graphing feature

• The table feature

• The equation solver

• The statistical analysis

When approaching 3 from values larger than 3, what do the y-values of f(x) equal?

• -1

• 0

• -2

• 1

When approaching 3 from values smaller than 3, what do the y-values of f(x) equal?

• 1

• 0

• -2

• -1

What is the significance of the table feature being set to 'ask'?

• It solves equations automatically

• It allows manual input of x-values

• It displays the graph of the function

• It automatically calculates all values