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