Translation and Reflection

When combining translations and reflections the order in which you do them is important.

A general rule for drawing the transformations:

First - Apply Reflections

Second - Apply Translations

#1

On one axis graph y=x²

On the same axis graph y=-x²+3 in a different color

(Just in case the transformations are an x-axis reflection and a vertical shift up)

#2

Copy this graph onto an axis call it f(x)

On the same axis graph -f(x+1) in a different color

(Just in case the transformations are an x-axis reflection and a horizontal shift left)

#3

Copy this graph onto an axis call it g(x)

On the same axis graph g(-x)+2 in a different color

(Just in case the transformations are a y-axis reflection and a vertical shift up)