How to do a translation, followed by a reflection in the x-axis?

Question

For example if the parent function is f(x) = x²+2x+1, or f(x) = (x+1)² and the problem asks for a translation left 3, and down 1, followed by a reflection in the x-axis.

If I'm understanding correctly, g(x) = -f(x+3)-1

g(x) = -((x+3) +1)²

g(x) = -(x+4)²

Is this correct?

Answer 1

f(x)=(x+1)^2

left 3: f(x)=(x+1+3)^2, f(x)=(x+4)^2

down 1: f(x)=(x+4)^2-1

reflection in the x-axis: f(x)=-(x+4)^2-1