Graph Transformations: Af(B(x-c))+D

For y = √(x+3) - 5, the point (0,0) from y = √x becomes

(-3, -5)

For y = -3(x+4)²-5, the point (1,1) from y = x² becomes

(-3, -8)

For y=2(x-3)², the point (1, 1) from y= x² becomes

(4, 2)

For y = 3|x-5| +2, the point (1,1) from y = |x| becomes

(6,5)

f(Bx); |B| > 1

Horizontal squish by a factor of B

f(Bx); |B| < 1

Horizontal stretch by a factor of B

-f(x)

Reflects graph across x-axis

f(-x)

Reflects graph across y-axis

f(x)

parent function

f(x)-D

shifts graph down D units ( vertical shift)

f(x +C)

shifts graph left C units (horizontal shift)

f(x-C)

shifts graph right C units (horizontal shift)

f(x) + D

shifts graph up D units (vertical shift)

Af(x); |A| < 1

vertical squish by a factor of A

Af(x); |A| > 1

vertical stretch by a factor of A