Transformations and Key Features

(0, -3)

(0, 1)

(0, 3)

(2, 1)

x

y

d

r

x

y

d

r

y=1

x=0

All Real Numbers

x>0

y > 0

x> 0

All Real Numbers

y > 1

all real numbers

y > -1

y < -1

x > -1

all real numbers

y > 3

y < 3

x > 3

all real numbers

y > 3

y < 3

x > 3

3 Units Up

3 Units Down

3 Units Left

3 Units Right

translation of $$f\left(x\right)=x^2$$ up 2 units.

translation of $$f\left(x\right)=x^2$$ down 2 units.

translation of $$f\left(x\right)=x^2$$ left 2 units.

translation of $$f\left(x\right)=x^2$$ right 2 units.

translation of $$f\left(x\right)=x^2$$ up 1 unit.

translation of $$f\left(x\right)=x^2$$ down 1 unit.

translation of $$f\left(x\right)=x^2$$ left 1 unit.

translation of $$f\left(x\right)=x^2$$ right 1 units.

translation of $$f\left(x\right)=x^2$$ up 8 units.

translation of $$f\left(x\right)=x^2$$ down 8 units.

translation of $$f\left(x\right)=x^2$$ left 8 units.

translation of $$f\left(x\right)=x^2$$ right 8 units.

dilation of $$f\left(x\right)=x^2$$ stretched vertically.

dilation of $$f\left(x\right)=x^2$$ compressed vertically.

dilation of $$f\left(x\right)=x^2$$ stretched horizontally.

dilation of $$f\left(x\right)=x^2$$ compressed horizontally.

g(x) = x² - 5

g(x) = x² + 5

g(x) = (x - 5)²

g(x) = (x + 5)²

g(x) = x² - 3

g(x) = x² + 3

g(x) = (x - 3)²

g(x) = (x + 3)²

(2, -6)

(2, 2)

(-2, -2)

(6, -2)

Wider

(Vert. Compress)

Narrower

(Vert. Stretch)

Wider

(Vert. Compress)

Narrower

(Vert. Stretch)

Reflected over x and down 3