Learn: Pre Calc Transformations

vertical shift up

y=f( x)+c

add c to function

every point moves up c

vertical shift down

y=f(x)-c

subtract c from function

every point moves down c

horizontal shift left

y=f(x+c)

replace x x+c

every point moves left c units

horizontal shift right

y=f(x-c)

replace x with x-c

every point moves right c units

y-axis reflection

y=f(-x)

replace x with -x

every x coordinated changes to its opposite

x-axis reflection

y= -f(x)

multiply function by -1

every y coordinate changes to its opposite

vertical stretch

y=kf(x)

multiply function by k

every y coordinate is multiplied by k

vertical compression

y=1/kf(x)

multiply function by 1/k

every y coordinate is multiplied by 1/k

horizontal compression

y=f(kx) k>1

replace x with kx

every x coordinate is divided by k

horizontal stretch

y=f(1/kx) k>1

replace x with 1/k x

every x coordinate is divided by 1/k

(or multiplied by k)