Reflections
Shifting
Dilation
Rules
Combined
100
-f(x)
Reflecting across the x axis
100
f(x+2)
Shifting left 2 units
100
2f(x)
Vertical Stretch
100
How do i know if I am reflecting?
If I see a negative in front or inside the function
100

f(x+2) - 2

The function shifts 2 units left and 2 units down

200
f(-2x)
Reflecting across the y axis
200
f(x) + 2
Shifting 2 units up
200
1/2f(x)
Vertical Compression
200

When you multiply the function by a number greater than 1, example. 4x2, what is the transformation?

Vertical Stretch

200

f(x-2)+1

The function shifts 2 units right and one unit up

300
-1/2f(x)
Reflecting across the x axis
300
f(x-3)
Shifting 3 units right
300
f(2/3x)
horizontal stretch
300

How is it different shifting / moving a function left and right?

To shift left it is a function (x + 2) and to shift right is a function (x -2)  OR

if shifting to the left --> Add

if shifting to the right --> subtract

300

-f(x+1)

The function reflects across the x axis, shifting one unit to the left

400
f(-2/3x)
Reflecting across the y axis
400
f(x) - 5
shifting 5 units down
400
f(2x)
horizontal compression
400

When you multiply the function by a fraction ex. 1/4x2, what is the transformation?

Vertical Compression or Vertical Shrink

400

-f(x)+4

The function is reflected across the X-axis and shifted 4 units up

500
-2f(-2x)
Reflecting across the x and y axis
500
f(x-2) +1
Shifting 2 units right and one unit up
500
2f(1/2x)
Rarely ever seen, however the two transformations are vertical stretch and horizontal stretch
500

When you multiply the function by a fraction inside and outside ex. 1/4(1/2x)2, what is the transformation?

Vertical Compression and Horizontal Stretch

500

f(-x+4)

The function is reflected across y axis, and shifts 4 units to the left

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