Square brackets traditionally meant the greatest integer function, now called the floor function.
So y = [2x - 5] = Floor(2x - 5) = ⌊2x - 5⌋ where there are little hooks on the bottom of the container glyphs.
Here's a GeoGebra graph:
Find the x-intercept and determine where the graph is increasing and where it is decreasing.
The x-intercept is a line segment: y = 0 for 2.5 ≤ x < 3.
From Wolfram, "A function f(x) increases on an interval I if f(b) ≥ f(a) for all b > a, where a,b in I."
So y = Floor(2x - 5) is increasing on the interval (-∞,∞).
If the function was meant to be the absolute value function,
y = |2x - 5|
y = 2 | x - 5/2 |
which is y = |x| stretched by 2 times in the y-direction and shifted right by 5/2.
The graph is increasing on the interval (5/2, ∞) and
decreasing on the interval (-∞, 5/2).
The x-intercept is x = 5/2, the location of the vertex.
Here's a graph: