Graphing: Transformations

How to interpret and use transformations when graphing.

y = f(x) + k

Vert. Translation:
- if k > 0 → upward k units.
- if k < 0 → downward k units.
(x, y) → (x, y+k)

y = f(x+h)

Horiz. Translation:
- if k > 0 → left h units.
- if k < 0 → right h units.
(x, y) → (x+h, y)

y = -f(x)

Reflection in the x-axis.
(x, y) → (x, -y)

y = f(-x)

Reflection in the y-axis.
(x, y) → (-x, y)

x = f(y)

Inverse Function: Reflection in line y=x.
(x, y) → (y, x)

y = af(x)

Vert. Stretch:
- if a > 1 vert. expansion by factor of a.
- if a < 1 vert. compression by factor of a.
(x, y) → (x, ay)

y = f(kx)

Horiz. Stretch:
- if k > 1 horiz. compression by factor of 1/k.
- if k < 1 horiz. expansion by factor of 1/k.
(x, y) → (x/k, y)