Part 5/6:
Example of Vertical Shift
Shift Up: Transforming to ( f(x) + 2 ) results in shifting the parabola up by 2 units.
Shift Down: Conversely, ( f(x) - 2 ) would shift it down by 2 units.
Example of Horizontal Shift
Shift Left: Transforming to ( f(x + 2) ) shifts the entire parabola left by 2 units.
Shift Right: On the other hand, ( f(x - 2) ) shifts it right by 2 units.
Combining Transformations
Often, functions involve both vertical and horizontal shifts. For instance, consider the transformation of ( g(x) = f(x - 3) + 16 ). This indicates a shift right by 3 units and then a vertical shift up by 16 units. Observing the parabolic nature of the function helps to visualize these shifts effectively.