Question

Which is the graph of y = [x] - 2?

Answer 1

Answer: Top row, third option (far right)

Explanation:

The notation $\lfloor x \rfloor$ means "floor of x". Whatever decimal value x is, we just ignore the decimal portion and just focus on the integer part. We round down to the nearest whole number. We always round down.

For something like x = 2.5 or x = 2.7, the value of $\lfloor x \rfloor$ will be 2. It doesn't matter that 2.7 is closer to 3 than it is to 2. The interval $2 \le x < 3$ will be entirely on the x axis since we are taking the result of the flooring operation and subtracting off 2. Notice how x = 3 is not included. This is because x = 3 leads to y = 1 instead of y = 0. So we have an open hole at the end of the interval. The same goes for any other piece as well.

Answer 2

Answer:

The Third option [ far right]