Please explain the graph of int(x)

The line represents the integer values and the circles represent the non-integer values. This graph helps to visualize how the greatest integer function works.In summary, the conversation discusses the representation of the greatest integer function using a line and a circle. The line represents the integer values and the circles represent the non-integer values. This graph helps to visualize the behavior of the function.
  • #1
Curd
78
1
i do not understand why they graph it with a line and a circle. I know what the circle and the line mean, i just do not understand how they apply to this graph.
 
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  • #2
Curd said:
i do not understand why they graph it with a line and a circle. I know what the circle and the line mean, i just do not understand how they apply to this graph.
Are you talking about the greatest integer function that looks like this?
[tex]\lfloor x\rfloor[/tex]

If so, the greatest integer function is defined as the largest integer that is less than or equal to x.
[tex]\lfloor 2.0\rfloor = 2[/tex]
[tex]\lfloor 2.5\rfloor = 2[/tex]
[tex]\lfloor 2.99\rfloor = 2[/tex]
[tex]\lfloor 3.0\rfloor = 3[/tex]

The function has a jump of one unit at each integer value.
 

What does "int(x)" mean in a graph?

"int(x)" in a graph refers to the integer value of the x coordinate. This means that the x value on the graph is a whole number, and does not have any decimal or fractional components.

How is "int(x)" different from "x" on a graph?

The difference between "int(x)" and "x" on a graph is that "x" represents the exact value of the x coordinate, including any decimal or fractional components. "int(x)", on the other hand, represents the integer value of the x coordinate, which is rounded down to the nearest whole number.

Why is "int(x)" used in some graphs?

"int(x)" is used in some graphs to represent discrete data or to highlight specific points on the graph that have integer coordinates. It can also be used to simplify the graph and make it easier to read by removing unnecessary decimal values.

Can "int(x)" be negative in a graph?

Yes, "int(x)" can be negative in a graph. This means that the x coordinate is a negative integer, such as -1, -2, -3, etc. It is important to pay attention to the scale of the graph to determine the exact value of the negative integer.

How is "int(x)" calculated in a graph?

"int(x)" is calculated by rounding down the x coordinate to the nearest integer. This means that if the x coordinate is already a whole number, the "int(x)" value will remain the same. However, if the x coordinate has decimal or fractional components, they will be disregarded and the "int(x)" value will be the integer part of the number.

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