Transformations of Special Functions

horizontal Shift left 2 units

Describe the transformation from

horizontal shift right 5 units

Describe the transformation from y = cube root of x to the function y = cube root of (x-5)

horizontal shift right 2 units

Describe the transformation from y = x² to the function on the left.

vertical shift 6 units up

Describe the transformation from y = x² to the function on the left.

Vertical stretch by a factor of 3 (graph becomes narrower)

Describe the transformation from y = x² to the y = 3x²

vertical Shift up 1 unit

Describe the transformation from y = x² to y = x² + 1

A vertical shift down 1 unit

Describe the transformation from y = x² to y = x² - 1

horizontal shift to the left 1 unit

Describe the transformation from y = x² to y =(x + 1)²

vertical shift down 7 units

Describe the transformation from y = x³ to the function on the left.

vertical shift up 5 units

Describe the transformation from y = x³ to the function on the left.

Vertical compression by factor of 1/4 (graph becomes wider)

Describe the transformation from y = x³ to the function y = (1/4) x³

vertical stretch by a factor of 8 (graph will become narrower)

Describe the transformation from y = x³ to the function y = 8x³

horizontal shift to the right 2 units

Describe the transformation from y = x³ to y =( x - 2)³

Point down

Describe the transformation from y = √x to the function on the left y = -√x.

horizontal shift left 6 units

Describe the transformation from y = √x to the function y = √(x+6)

horizontal shift left 5 units

Describe the transformation from y =|x| to the function y =|x+5|

horizontal Shift right 1 unit

Describe the transformation from y =|x| to the function y =|x-1|

Point down and steeper

Describe the transformation from y =√x to the function on y= -2√x.

vertical shift 5 units down

Describe the transformation from y=x to y=x-5

Reflect over x-axis and horizontal shift left 2 units

Describe the transformations from y = x³ to the function on the left.

horizontal shift right 3 units and vertical shift up 4 units

Describe the transformations from y = x³ to the function y = (x - 3)³ + 4

horizontal shift right 7 units; vertical shift down 1 unit

Describe the transformations from y = √x to the function y = √(x-7) - 1

Point down, shift down 3

Describe the transformations from y =|x| to the function y=- .5|x| - 3

horizontal shift right 4 units ; vertical shift up 2 units

Describe the transformations from y =|x| to the function y=|x+4| + 2

horizontal shift left 8 units; vertical shift up 5 units

Describe the transformations from y =|x| to the function y=|x+8| + 5

linear left 3 and down 1

y = (x + 3) - 1

linear right 1 and up 3

y = (x - 1) + 3

Quadratic

y = -(x + 5)^2 + 4