Transformation of Graphs - reflection

The above animation shows the reflection of graphs. It is as follows:

f(x) → f(-x) is a reflection in the y-axis

f(x) → -f(x) is a reflection in the x-axis

E.g.

f(x) = x² - 2x

f(-x) = (-x)² - 2(-x) = x² + 2x

-f(x) = -(x² - 2x) = - x² + 2x