Part 3/6:
For example, if ( f(x) ) is represented on the graph, then for any point ( (x, f(x)) ), the new point after the transformation would be ( (x, f(x) + a) ).
Shifting Down
Conversely, if we express the transformation as ( y_2 = f(x) - a ), this results in the graph shifting downwards by ( a ) units. Every point on the graph moves vertically down by the value of ( a ).
Both these transformations are visually straightforward and primarily involve translating the graph up or down along the Y-axis.
Horizontal Shifts
Horizontal shifts are a bit more nuanced, as they involve manipulating the inside of the function's argument.