Question

Let f(x) = x^2+ sin x and let g(x) = ? where g is the function whose graph has been obtained from that of f by shifting it 2 to the right and 6 up.
I know you will probably have to use +6 outside of the function, but how do I shift this to the right?(I know I'll have to use -)

Answer 1

look at each individual function in f
x^2 shifted 2 units to your right will be (x-2)^2
sinx shifted 2 units to your right will be sin(x-2)
so f(x-2) which is shifting f 2 units to your right is you h
meaning \(h(x)=(x-2)^2+sin(x-2)\)
then we shift that f(x-2) 6 units upwards to get f(x-2)+6=g(x)

Answer 2

when you look at shifting look at it this way f(x) shifted k units to right
meaning f(x-k) if we want h units up we add f(x-k)+h
so for the opposite f(x+k) to left and down f(x)-h
left and down f(x+k)-h

Answer 3

Thanks a bunch! I think I had the (x-2)^2 thing down, I just didn't think to so sin(x-2).