Answer: Top right graph (option B)
Step-by-step explanation: The function ⌈x⌉ returns the integer number lower or equal than x, for example, if we have x = 3.5, then ⌈3.5⌉ = 3.
Here we have the equation y = 2*⌈x⌉ − 3
when x = 0, y = 2 ⌈0⌉ − 3 = -3, then we have the pair (0, -3)
and when x = 0.5, y = 2 ⌈0.5⌉ − 3 = -3, then we have the pair (0, -3)
when x = 1, y = 2 ⌈1⌉ − 3 = -1, now we have the pair (1, -1)
and when x = 1.43, y = 2 ⌈1,43⌉ − 3 = -1, now we have the pair (1, -1)
when x = 2, y = 2 ⌈2⌉ − 3 = 1, we have the pair (2, 1)
and when x = 2.8, y = 2 ⌈2.8⌉ − 3 = 1, we have the pair (2, 1)
Whit this information we can see that the possible graphs are A and B, where the difference between them is the position of the white dots. These dots select the range of x is where the function has the value in the graph (black dot means the start, and the white dot means the end)
In our case, for the 3 points we obtained we have that:
the value of y is -3 in the range of x =(0, 0.9999)
the value of y is -1 in the range of x = ( 1, 1.9999)
and so on, This means that the right answer is the option B (the top right graph)