Part 2/6:
Function transformations allow us to modify the graph of a basic function to create new graphs. The most fundamental of these transformations include shifting the graph vertically (up or down) or horizontally (left or right). This understanding serves as a foundation for more advanced transformations such as stretching and compressing functions, which will be addressed in future discussions.
Vertical Shifts
Vertical shifts occur when we add or subtract a constant from the function itself.
Shifting Up
When we express a function as ( y_1 = f(x) + a ) where ( a > 0 ), the graph of ( f(x) ) is shifted upwards by ( a ) units. In simpler terms, every point on the graph moves vertically up by the value of ( a ).