Graph Translations

y = f(x) to y = f(x) + a, where a > 0

Translate vertically up by a units

y = f(x) to y = f(x) + a, where a < 0

Translate vertically down by a units

y = f(x) to y = f(x + a), where a > 0

Translate horizontally left by a units

y = f(x) to y = f(x + a), where a < 0

Translate horizontally right by a units

y = f(x) to y = af(x), where a > 1

Stretch enlargement vertically by scale factor a

y = f(x) to y = af(x), where 0 < a < 1

Compression enlargement vertically by scale factor 1/a

y = f(x) to y = -f(x)

Reflection vertically in x-axis

y = f(x) to y = f(-x)

Reflection horizontally in y-axis

IxI+4

Up 4

IxI-3

Down 3

Ix+5I

Left 5

Ix-8I

Right 8

-IxI

Reflect over x - axis

(x-3)³+1

Right 3, up 1

x³+5

Up 5

(x+10)²

Left 10

√(x-4) -2

Right 4, down 2

f(x-6) -1

Right 6, down 1

f(x) +5

Up 5

f(x+2)

Left 2

3x+1

Stretch 3, up 1

2(x-2)+2

Stretch 2, right 2, up 2

0.5(x-4)-17

Compress 0.5, right 4, down 17