I would suggest graphing and , then using addition of ordinates to graph .
You are correct in identifying the intervals where the function behaves differently. Consider each interval in turn. For example, if x < 2, then x - 2 < 0, x - 3 < 0 and x - 4 < 0. For all a < 0, mod(a) = -a. (They usually write abs(a) for the "absolute value.") So, mod(x-2)+mod(x-3)+mod(x-4) = -(x - 2) - (x - 3) - (x - 4) = -x + 2 - x + 3 - x + 4 = -3x + 9. If 2 <= x < 3, then x - 2 >= 0, x - 3 < 0 and x - 4 < 0. Therefore, mod(x-2)+mod(x-3)+mod(x-4) = x - 2 - (x - 3) - (x - 4) = x - 2 - x + 3 - x + 4 = -x + 5. You have to do similar calculations for the remaining two intervals.
To draw a graph of y = -3x + 9 on the interval x < 2, you need to find two points and draw a line through them. For example, y = 9 for x = 0 and y = 0 for x = 3. You only need a part of that line that is located above the interval in question (marked in bold). Do a similar thing for the other three intervals.