Answer:
See attachment.
Explanation:
The double brackets [[x]] denote the function is a floor function.
It also (more commonly) written as ⌊x⌋.
The definition of a floor function is "the greatest integer that is less than or equal to x".
Parent floor function
f(x) = ⌊x⌋
The graph of the parent floor function has closed dots at (x, x) and open dots at (x, x-1). Each segment is joined with a horizontal line (step).
The closed dot means the value is included, whereas the open dot means the value is not included.
Given floor function:
g(x) = -[[x]] = -⌊x⌋
As the given floor function is negative, it is a reflection of the parent floor function in the x-axis.
Therefore, the graph of the given function has closed dots at (x, -x) and open dots at (x, -(x-1)). Each segment is joined with a horizontal line (step).
To draw the graph with the restricted domain [0, 5):
- Place closed dots at (0, 0), (1, -1), (2, -2), (3, -3) and (4, -4).
- Place open dots at (1, 0), (2, -1), (3, -2), (4, -3) and (5, -4).
- Join each pair of closed and open dots (with the same y-value) with a horizontal line (step).
Note
The first attachment (green graph) is the graph of the given function g(x).
The second attachment (black graph) is the graph of the parent floor function for information purposes only.