Sure, let’s analyze the points to see which ones are on the graph of the function [tex]\( f(x) = \lfloor x \rfloor + 2 \)[/tex]. Here, [tex]\(\lfloor x \rfloor\)[/tex] denotes the greatest integer less than or equal to [tex]\( x \)[/tex].
1. Point (-3.8, -2):
- The greatest integer less than or equal to -3.8 is -4.
- Applying the function: [tex]\( f(-3.8) = -4 + 2 = -2 \)[/tex].
- So, the point (-3.8, -2) is on the graph.
2. Point (-1.1, 1):
- The greatest integer less than or equal to -1.1 is -2.
- Applying the function: [tex]\( f(-1.1) = -2 + 2 = 0 \)[/tex].
- So, the point (-1.1, 1) is not on the graph (as [tex]\( f(-1.1) = 0 \)[/tex]).
3. Point (-0.9, 2):
- The greatest integer less than or equal to -0.9 is -1.
- Applying the function: [tex]\( f(-0.9) = -1 + 2 = 1 \)[/tex].
- So, the point (-0.9, 2) is not on the graph (as [tex]\( f(-0.9) = 1 \)[/tex]).
4. Point (2.2, 5):
- The greatest integer less than or equal to 2.2 is 2.
- Applying the function: [tex]\( f(2.2) = 2 + 2 = 4 \)[/tex].
- So, the point (2.2, 5) is not on the graph (as [tex]\( f(2.2) = 4 \)[/tex]).
5. Point (4.7, 6):
- The greatest integer less than or equal to 4.7 is 4.
- Applying the function: [tex]\( f(4.7) = 4 + 2 = 6 \)[/tex].
- So, the point (4.7, 6) is on the graph.
Based on these calculations, the points that are on the graph of the function [tex]\( f(x) = \lfloor x \rfloor + 2 \)[/tex] are:
1. (-3.8, -2)
2. (4.7, 6)
Therefore, the points (-3.8, -2) and (4.7, 6) are the ones that lie on the graph of the function.
