Answer:
B, C, D
Step-by-step explanation:
What you have here is a step function, which usually looks like a set of stairs. A really common form of the step function is called the greatest integer function, y = [x], which for all values of x returns the largest possible integer less than or equal to x. When you see the brackets in a function like this, it just means to round down to the nearest integer value; for example, f(3.9) = [3.99] = 3. But, anyway, choice C is automatically correct because this is in fact a graph of the y = [x].
For a graph to be one-to-one, it has to pass both the vertical line test and the horizontal line test. This graph passes the vertical line test but fails the horizontal line test because it has constant values/straight horizontal lines that make it fail.
For the rest, you just have to know that this is the graph of f(x) = [x]. With that, you just take their x values, plug it in, and round down to the nearest integer to see if the choice is correct.
f(-3.2) = -3
Think [-3.2]. If you have to round down to the nearest integer, it will actually be -4; if you were to round to -3, you would actually be rounding up, since -3 is greater than -3.2 on a number line. Always try to visualize it on a number line if you aren't sure what to round down to. Choice A is not correct.
f(0.6) = 0
This is correct. You have to round down to the nearest integer, which is 0.
f(5.1) = 5
This is correct. You have to round down to the nearest integer, which is 5.
