Graph y=[x+2]

To graph the equation y = [x+2], we need to plot points on a coordinate plane that satisfy the equation.

By definition, [x] represents the greatest integer less than or equal to x. So, in this case, [x+2] represents the greatest integer less than or equal to (x+2).

We can break it down into different intervals:

For values of x that are less than -1, [x+2] is always -1. So we have a horizontal line y = -1 for x < -1.

For values of x between -1 and 0 (exclusive), [x+2] is 0. Meaning, y = 0 within this interval.

For values of x between 0 and 1 (exclusive), [x+2] is 2. Meaning, y = 2 within this interval.

For values of x between 1 and 2 (exclusive), [x+2] is 3. Meaning, y = 3 within this interval.

For values of x that are greater than or equal to 2, [x+2] is always the whole number part of x+2. For example, if x = 2.3, then [x+2] = 4. If x = 3.8, then [x+2] = 5, and so on. This interval goes on and on with every integer greater than or equal to 2.

So, graphically, the function y = [x+2] consists of individual horizontal lines at y = -1, y = 0, y = 2, y = 3, y = 4, y = 5, and so on, depending on the interval.

Here is a rough sketch of the graph:

| | | |
| | | |
5 | | | |
| | | |
4 | | | |
| | | |
3 | | | |
| | | |
2 | | | |
| | | |
1 | | | |
| | | |
0 | | | |
| | | |
-1 |-------|-------|-------|
-2 -1 0 1