Given:
[tex]f(x)=(x-5)^2+2[/tex][tex]g(x)=(x+6)^2-4[/tex]Required:
We need to find the transformation.
Explanation:
Consider the function.
[tex]g(x)=(x+6)^2-4[/tex]Replace x =x-11 in the function.
[tex]g(x-11)=(x-11+6)^2-4[/tex][tex]g(x-11)=(x-5)^2-4[/tex]Add 6 to both sides of the equation.
[tex]g(x-11)+6=(x-5)^2-4+6[/tex][tex]g(x-11)+6=(x-5)^2+2[/tex][tex]Substitute\text{ }f(x)=(x-5)^2+2\text{ in the equation.}[/tex][tex]g(x-11)+6=f(x)[/tex][tex]f(x)=g\mleft(x-11\mright)+6[/tex]We know that if f(x)=g(x-k)+h the g(x) shifts k units left and h and shifts h units above.
Here the graph of g (x) is shifted 11 units above and 6 units to the left to the graph of f(x).
Final answer:
The graph of g (x) is shifted 11 units above and 6 units to the left to the graph of f(x).
