Before: y = f(x)

After: y = f(x + a)

(x, y) → (x + a, y)

Example:

y = f(x) (5,4)

y = f(x - 3)

Before: (5,4)

After: (8,4)

Before: y = f(x)

After: y = f(x) + a

(x, y) → (x, y + a)

Example:

y = f(x) (5,4)

y = f(x) - 3

Before: (5,4)

After: (5,1)

Before: y = f(x)

After: y = f(ax)

(x, y) → (x/a, y)

Example:

y = f(x) (5,4)

y = f(3x)

Before: (5,4)

After: (5/3,4)

Before: y = f(x)

After: y = af(x)

(x, y) → (x, ay)

Example:

y = f(x) (5,4)

y = 3f(x)

Before: (5,4)

After: (5,12)

Before: y = f(x)

After: y = -f(x)

(x, y) → (x, -y)

Before: y = f(x)

After: y = f(-x)

(x, y) → (-x, y)