Answer: The correct option is B.
Explanation:
From the given figure it is noticed that the parent function is,
[tex]f(x)=x^2[/tex]
The graph of f(x) shifts 5 units right.
The transformation is defined as,
[tex]g(x)=f(x+a)+b[/tex]
Where, a shows the horizontal shifts and b shows the vertical shift.
If a<0 then the graph of f(x) shifts right side by a units and if a>0 then the graph of f(x) shifts left side by a units.
If b<0 then the graph of f(x) shifts downward by b units and if b>0 then the graph of f(x) shifts upward by b units.
Since the graph of parent function is shifts only right side by 5 units, therefore
[tex]g(x)=f(x-5)+0[/tex]
Since [tex]f(x)=x^2[/tex]
[tex]g(x)=(x+5)^2[/tex]
Thus, the correct option is B.
The function in option A represents the left shift of f(x) by 5 units. The option C represents the downward shift of f(x) by 5 units. The option D represents the upward shift of f(x) by 5 units.
