Graphing Greatest Integer Functions

This video tutorial demonstrates how to graph two functions, f(x) = ⌊x⌋ - 2 and f(x) = ⌊x - 3⌋, using a TI-84 graphing calculator. It covers the steps to input the functions, adjust the graphing window, and interpret the graph's endpoints. The tutorial also explains how to verify function values using the calculator's table feature, ensuring accurate graph representation.

What is the primary function of the TI-84 calculator in this lesson?

• To perform statistical analysis

• To calculate derivatives

• To graph greatest integer functions

• To solve algebraic equations

What is the effect of subtracting 2 from the greatest integer function [x]?

• Shifts the graph left by 2 units

• Shifts the graph down by 2 units

• Shifts the graph up by 2 units

• Shifts the graph right by 2 units

How do you adjust the graphing window on the TI-84 for a better view?

• Use the 'Zoom' function

• Select 'Graph' from the main menu

• Change the min and max values in the 'Window' settings

• Press the 'Trace' button

What is the significance of open and closed points in the graph of a greatest integer function?

• They distinguish between included and excluded values at endpoints

• They represent the continuity of the function

• They show where the function is increasing or decreasing

• They indicate the start and end of the graph

How can you verify the graph of a function using the TI-84 calculator?

• By comparing with a textbook example

• By using the 'Zoom' feature

• By using the 'Trace' and 'Table' features

• By recalculating the function manually

What happens to the function value when x is 1 for f(x) = [x] - 2?

• It becomes 0

• It decreases to -3

• It remains at -2

• It jumps to -1

In the second example, what is the initial value of the function f(x) = [x - 3] at x = 0?

• 3

• 0

• -2

• -3

What is the effect of subtracting 3 from x in the function f(x) = [x - 3]?

• Shifts the graph up by 3 units

• Shifts the graph right by 3 units

• Shifts the graph down by 3 units

• Shifts the graph left by 3 units

How do the segments of the graph shift as you move to the right for f(x) = [x - 3]?

• They shift left by one unit

• They remain constant

• They shift down by one unit

• They shift up by one unit

What is the pattern of open and closed points for the function f(x) = [x - 3]?

• Open on both sides

• Closed on the left, open on the right

• Closed on both sides

• Open on the left, closed on the right