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


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