Question

Which equation represents the graph y=cos x flipped across the x-axis shifted vertically down by 2 units?

A. y=cos(-x)+2
B. y=cos (x-2)
C. y=cos x-2
D. y=-cos x-2

I think it is D. y=-cos x-2 please explain. Thank you!

Answer 1

It is D, When you reflect by the x-axis, you multiply the entire expression by -1, however if reflected by y-axis you multiply the independent variable by -1. Now same goes here with the translations, When u translate vertically, you add or subtract that value from the entire expression, However when you translate horizontally you add or subtract it by the independent variable but in the opposite way, So im gonna make an example and you can see how they applied,
reflect by y-axis, shift horizontally to the right by 2
==> y= cos(-(x-2))
I hope that kinda makes it clear