Answer:
The correct option is A.
Step-by-step explanation:
The given functions are
[tex]f(x)=x^2[/tex]
[tex]g(x)=-\frac{1}{5}(x-3)^2[/tex]
It can be written as
[tex]g(x)=-\frac{1}{5}f(x-3)[/tex] .... (1) [tex][\because f(x-3)=(x-3)^2][/tex]
The transformation is defined as
[tex]g(x)=kf(x+a)^2+b[/tex] .... (2)
Where, k is vertical stretch or compression, a is horizontal shift and b is vertical shift.
If |k|>1, then the graph stretch vertically and if 0<|k|<1, then graph compressed vertically.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
From equation (1) and (2), we get
[tex]k=-\frac{1}{5}, a=-3, b=0[/tex]
Here the negative means, the graph of f(x) flipped over the x-axis.
Since 0<|k|<1, therefore the graph compressed vertically.
The value of a is -3<0, so graph shifts 3 units right.
The graph of f(x) is the graph of g(x) compressed vertically, flipped over the x-axis, and shifted 3 units to the right.
Therefore the correct option is A.
