F(x) notations and their meaning

HORTIZONTAL TRANSLATION

F(x-h)

g(x)=(x-5)⁴→5 units right

g(x)=(x+2)⁴ → 2 units left

VERTICAL TRANSLATION

F(x)+k

g(x)=x⁴+1 →1 unit up

g(x)=x⁴-4 → 4 units down

REFLECTION

f(-x)

EXAMPLE: g(x)=(-x)⁴=x⁴ over y-axis

-f(x)

EXAMPLE: g(x)= -x⁴ over x-axis

HORIZONTAL STRETCH OR SHRINK

f(ax)

EXAMPLES:

g(x)=(2x)⁴ → shrink by a factor of ½

g(x)=(1/2x)⁴ → stretch shrink by a factor of 2

VERTICAL STRETCH OR SHRINK

a(f(x))

EXAMPLES
g(x)=8×⁴ → STRETCH BY A FACTOR OF 8

g(x)=1/4x^{4 →} SHRINK BY A FACTOR OF ¼