When you alter a graph, youtransformit. If you transform a graph without changing its shape, youtranslateit. Vertical and horizontal transformations are translations. Wheny = f(x) + d, shift (translate) the graph ofy = f(x)vertically (upward ifd > 0, downward ifd < 0).

Example:1. Problem: TranslateYou have been asked to shift the graph upwardy = x2upward by1. Solution:1. Rewrite the equation to do this, and then graph.y = x2 + 1The figure below is a graph of the solution.

Wheny = f(x + c), translate the graph ofy = f(x)horizontally (left ifc > 0, right ifc < 0).

Example:2. Problem: Sketch the graph ofFirst, graphy = |x + 2|. Solution:y = |x|, then shift it to the left 2 places. The figure below is a graph of the solution.

I saw this online and i was wondering how can you tell if it's a Horizontal Translation or Vertical one? If so, what are usually these translation used for?