Answer with explanation:
We are given a parent function f(x) by:
[tex]f(x)=x^2[/tex]
i.e. the graph of the function f(x) is a parabola with vertex at (0,0)
Also, we know that the transformation of the type:
f(x) → f(x+k)
is a shift or the translation of the function f(x) k units to the left or to the right depending on k.
if k>0 then the shift is k units to the left.
and if k<0 then the shift is k units to the right.
Here we have to graph the function:
f(x+3) i.e. k=3>0 i.e. the graph of this function is the shift of the graph of the function f(x) 3 units to the left.
i.e. the graph of f(x+3) is a upward open parabola with vertex at (-3,0).
i.e. [tex]f(x)=(x+3)^2[/tex]
