Transformation of Functions
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-f(x)
reflection over x-axis
f(-x)
reflection over y-axis
f(x) - 5
translation 5 units down
f(x + 5)
translation 5 units left
f(x - 5)
translation 5 units right
f(x) + 5
translation 5 units up
f(x+5)+5
translation 5 units up and 5 units left
f(x-5)+5
translation 5 units up and 5 units right
(1/5)f(x)
vertical compression
0.5f(x)+5
vertical compression and translation up 5
(-1/5)f(x)
vertical compression reflected over x-axis
5f(x)
vertical stretch
2f(x)+5
vertical stretch and translation up 5
-5f(x)
vertical stretch reflected over x-axis
