Algebra II Unit 8: Transforming Functions

Reflection over the x-axis

f(x) → -f(x)

Reflection over the y-axis

f(x) → f(-x)

Reflection over the origin

f(x) → -f(-x)

Even function

f(x) \= f(-x)

Odd function

f(x) \= -f(-x)

Horizontal shift

f(x) → (right) → f(x-a); f(x) → (left) → f(x+a)

Vertical shift

f(x) → (up) → f(x)+a; f(x) → (down) → f(x)-a

Horizontal dilations

f(x) → (stretch) → f(x/a); f(x) → (shrink) → f(ax)

Vertical dilations

f(x) → (stretch) → a*f(x); f(x) → (shrink) → f(x)/a