Remember the following rules for transformations of functions:
Vertical shift by c units (upwards):
[tex]f(x)\rightarrow f(x)+c[/tex]
Horizontal shift by c units (towards the right):
[tex]f(x)\rightarrow f(x-c)[/tex]
Vertical stretch by a factor c:
[tex]f(x)\rightarrow c\cdot f(x)[/tex]
We can identify the following elements in the equation of y=3(x-1)^2+1 :
1.- Shift right 2 units.
2.- Vertical stretch by a factor of 3
3.- Shift up 1 unit.
The option that displays these transformation is option B.
Therefore, the answer is:
Option B)
Shift right 2 units, stretch by a factor of 3, then shift up 1 unit.
