A diagram that represents the graph of y = [x] - 2 include the following: C. graph C.
In Mathematics and Euclidean Geometry, a ceiling function is sometimes referred to as the least integer function of a real number (x) and it is the smallest integer that is not smaller than x. Additionally, a ceiling function is denoted by this mathematical symbol [x].
Based on the definition of a ceiling function f(x) = [x], we have the following steps;
f(x) = 0, for 0 ≤ x < 1
f(x) = -1, for -1 ≤ x < 0
f(x) = -2, for -2 ≤ x < -1
f(x) = -3, for -3 ≤ x < -2
f(x) = -4, for -4 ≤ x < -3
f(x) = -5, for -5 ≤ x < -4
Since the graph of the parent ceiling function f(x) = [x] was vertically shifted down 2 units to produce the graph of y = [x] - 2, a step that would be included in the graph of this ceiling function is given by;
0 ≤ x < 1 → y = -2.
f(x) = -2, for, 0 ≤ x < 1.
In conclusion, the graph of this ceiling function y = [x] - 2, must hav a y-intercept at (0, -2) as correctly depicted by graph C only.