1. describe the transformations necessary to transform the graph of
f(x) to that of g(x)
f(x) = x² and g(x) = 3(x - 1)² + 4

- The function must be shifted right 1 unit.

- The function  must be shifted up 4 units.

- The function  must be stretched vertically by a factor of 3.

Step-by-step explanation:

There are some transformations for a function f(x):

If , then the function is shifted up "k" units.

If , then the function is shifted down "k" units.

If , then the function is shifted left "k" units.

If , then the function is shifted right "k" units.

If and , then the function is stretched vertically by a factor of "b".

If and , then the function is compressed vertically by a factor of "b".

In this case we have the following parent function :

And the function :

Based on the explained before, we can describe  the transformations necessary to transform the graph of  to the graph of :

- The function must be shifted right 1 unit.

- The function  must be shifted up 4 units.

- The function  must be stretched vertically by a factor of 3.