AP Precalc Function Transformations (copy) (copy)

For DFA AP Precal

horizontal shift left

f(x + c)

horizontal shift right

f(x - c)

vertical shift up

f(x) + c

vertical shift down

f(x) - c

reflection over x-axis

-f(x)

reflection over y-axis

f(-x)

vertical stretch

c · f(x), but c>1

vertical shrink

c · f(x), but 0<c<1

horizontal shrink

f(c · x), but c>1

horizontal stretch

f(c · x), but 0<c<1

x-values

horizontal transformations affect the _________.

y-values

vertical transformations affect the _________.

vertical dilation

(x, y) —> (x, c · y)

horizontal dilation

(x, y) —> (x/c, y)

horizontal shift left

(x, y) —> (x - c, y)

horizontal shift right

(x, y) —> (x + c, y)