Transforming Graphs

3 Units Up

3 Units Down

3 Units Left

3 Units Right

2 Units Up

2 Units Down

2 Units Left

2 Units Right

5 Units Up

5 Units Down

5 Units Left

5 Units Right

6 Units Up

6 Units Down

6 Units Left

6 Units Right

Vertically Stretched by a factor of 3

Vertically Stretched by a factor of $$\frac{1}{3}$$  

Horizontally Stretched by a factor of 3

Horizontally Stretched by a factor of $$\frac{1}{3}$$  

Vertically Stretched by a factor of $$\frac{1}{3}$$  

Vertically Stretched by a factor of $$3$$  

Horizontally Stretched by a factor of $$\frac{1}{3}$$  

Horizontally Stretched by a factor of $$3$$  

Reflected in the x-axis

2 Units Up

Reflected in the x-axis

2 Units Down

Reflected in the y-axis

2 Units Up

Reflected in the y-axis

2 Units Down

Reflected in the x-axis

4 Units Left

Reflected in the x-axis

4 Units Down

Reflected in the y-axis

4 Units Left

Reflected in the y-axis

4 Units Down

Vertically stretched by a factor of 2, right 3, and up 1

Vertically stretched by a factor of 1/2, left 3 and down 1

Vertically stretched by a factor of 1/2, right 3, and down 1

Vertically stretched by a factor of 2, left 3, and up 1

This graph has been reflected in the x-axis and y-axis, shifted to the left two units, and shifted down three units.

This graph has been reflected in the y-axis, shifted to the right by two units, and shifted down three units.

This graph has been reflected in the x-axis and y-axis, shifted to the left two units, and shifted up three units.

This graph has been reflected in the x-axis and y-axis, shifted to the right two units, and shifted down three units.

$$y=\left|11x+2\right|-4$$

$$y=\left|x\right|$$  

$$y=11\left|x-2\right|+4$$  

$$y=11\left|x+2\right|+4$$

Vertical translation by d units up

Vertical ranslation by d units down

Horizontal translation by d units left

Horizontal translation by d units right

Vertical translation by d units up

Vertical translation by d units down

Horizontal translation by d units left

Horizontal translation by d units right

Translation in y direction by c units up

Translation in y direction by c units down

Translation in x direction by c units left

Translation in x direction by c units right

Translation in y direction by c units up

Translation in y direction by c units down

Translation in x direction by c units left

Translation in x direction by c units right

Reflection in the

y-axis

Reflection in the

x- axis

Translation in y direction

Translation in x direction

Reflection in the

y-axis

Reflection in the

x-axis

Translation in the y direction

Translation in the x direction

Stretch in y direction by scale factor a

Stretch in y direction by scale factor 1/a

Stretch in x direction by scale factor a

Stretch in x direction by scale factor 1/a

Stretch in y direction by scale factor b

Stretch in y direction by scale factor 1/b

Stretch in x direction by scale factor b

Stretch in x direction by scale factor 1/b