Question

what transformation occurs(vertically stretched, vertically compressed, reflection, translation, rotation, etc) happens when a function , f(x) is turned into -f(x).

Answer 1

Answer: reflection over x axis

g(x) = -f(x) is the same as g(x) = -1*f(x)

Since y = f(x), we are really saying g(x) = -1*y. Whatever the y coordinate is on f(x), multiply it by -1. This turns something like y = 2 into y = -2, or something like y = -3 into y = 3, etc etc. Visually this reflects the point over the horizontal x axis. Do this to all points on f(x), and the entire curve reflects over the x axis.

I show an example of y = x^2 turn into y = -x^2 in the attached image below.