Answer :
1.
[tex]g(x)=(x-4)^2-1[/tex]
[tex]f(x)[/tex] was moved 4 units right and 1 unit down
2.
[tex]f(x)=x^2\\ g(x) = x^2 + 3[/tex]
[tex]f(x)[/tex] was moved 3 units up
3.
[tex]f(x)=x^2\\ g(x)=\dfrac{1}{4}(x-6)^2+8[/tex]
[tex]f(x)[/tex] was moved 6 units right, scaled down along the y-axis 4 times and moved 8 unit up
4.
[tex]f(x)=x^2\\ g(x)=-(x-3)^2+2[/tex]
[tex]f(x)[/tex] is moved 3 units right, reflected over the x-axis and moved 2 units up
[tex]g(x)=(x-4)^2-1[/tex]
[tex]f(x)[/tex] was moved 4 units right and 1 unit down
2.
[tex]f(x)=x^2\\ g(x) = x^2 + 3[/tex]
[tex]f(x)[/tex] was moved 3 units up
3.
[tex]f(x)=x^2\\ g(x)=\dfrac{1}{4}(x-6)^2+8[/tex]
[tex]f(x)[/tex] was moved 6 units right, scaled down along the y-axis 4 times and moved 8 unit up
4.
[tex]f(x)=x^2\\ g(x)=-(x-3)^2+2[/tex]
[tex]f(x)[/tex] is moved 3 units right, reflected over the x-axis and moved 2 units up