Answer:
The correct option is b.
Step-by-step explanation:
The given function are
[tex]f(x)=x^3[/tex]
[tex]g(x)=(x+1)^3[/tex]
From the given function,we get
[tex]g(x)=f(x+1)[/tex] .... (1)
The transformation of f(x) is defined as
[tex]g(x)=f(x+a)+b[/tex] ... (2)
Where, a represents the horizontal shift and b represents the vertical shift.
If a>0, the graph of f(x) shifts a units left and if a<0, the graph of f(x) shifts a units right.
If b>0, the graph of f(x) shifts b units upward and if b<0, the graph of f(x) shifts b units downward.
On comparing (1) and (2), we get
[tex]a=1,b=0[/tex]
Since a=1>0, therefore the graph of g(x) is a horizontal transformation of f(x), 1 unit to the left. Option b is correct.
