Reversing the horizontal directionf(x + 3) means a translation 3 units to the left, not to the right.
Confusing −f(x) with f(−x)the first is a reflection in the x-axis, while the second is a reflection in the y-axis.
Putting a vertical translation inside the bracketa number added to the whole function sits outside the bracket.
Applying transformations in the wrong orderreview the order of the steps before drawing, especially when there are transformations inside the bracket.