Absolute Value Function Transformations
Absolute Value Function Transformations
Absolute Value Function Transformation Exercise
The absolute value function is y = |x| , denoted by function g.
The transformed basic function is y = a|bx - h| +k.
Note: The 'slider' feature on the x-y coordinate plane can be used to change the a, b, h, and k values
for the following exercises. To do so, place the cursor and hold it on the dot of the slider and
slide it to the desired m and b values.
To move the slider to a different location on the x-y plane, place the cursor and hold it on the line
of the slider and move it to the desired location.
Note: You can zoom in or out with the mouse.
Exercise 1
Perform the following absolute value function transformation:
Vertical shift of 3 units up.
The new function is y=|x| +3 , denoted by function f.
Set a=1. Set b=1.
Set h=0 since there is no horizontal shift
Set k=3 which represents the vertical shift of 3 units up.
Observe the transformation of the absolute value function.
Exercise 2
Perform the following absolute value function transformation:
Vertical shift of 3 units down.
The new function is y=|x| - 3 , denoted by function f.
Set a=1. Set b=1.
Set h=0 since there is no horizontal shift
Set k= - 3 which represents the vertical shift of 3 units down.
Observe the transformation of the absolute value function.
Exercise 3
Perform the following absolute value function transformation:
Horizontal shift of 3 units to the right.
The new function is y=|x-3| , denoted by function f.
Set a=1. Set b=1.
Set h=3 which represents the horizontal shift of 3 units to the right.
Set k=0 since there is not vertical shift.
Observe the transformation of the absolute value function.
Exercise 4
Perform the following absolute value function transformation:
Horizontal shift of 3 units to the left.
The new function is y=|x+3| , denoted by function f.
Set a=1. Set b=1.
Set h=- 3 which represents the horizontal shift of 3 units to the left.
Set k=0 since there is not vertical shift.
Observe the transformation of the absolute value function.
Exercise 4
Perform the following absolute value function transformation:
Horizontal shift of 3 units to the left.
The new function is y=|x+3| , denoted by function f.
Set a=1. Set b=1.
Set h=- 3 which represents the horizontal shift of 3 units to the left.
Set k=0 since there is not vertical shift.
Observe the transformation of the absolute value function.
Exercise 5
Perform the following absolute value function transformation:
Vertical shift of 3 units up plus a horizontal shift of 3 units to the right.
New function: y = |x-3| +3 , denoted by function f.
Set a=1. Set b=1.
Set h=3 which represents the horizontal shift of 3 units to the right.
Set k=3 which represents the vertical shift of 3 units up.
Observe the transformation of the absolute value function.
Exercise 6
Perform the following absolute value function transformation:
Vertical shift of 3 units down plus a horizontal shift of 3 units to the left.
New function: y =|x+3| - 3 , denoted by function f.
Set a=1. Set b=1.
Set h=- 3 which represents the horizontal shift of 3 units to the left.
Set k=- 3 which represents the vertical shift of 3 units down.
Observe the transformation of the absolute value function.
Exercise 7
Perform the following absolute value function transformation:
Vertical shift of 3 units down plus a horizontal shift of 3 units to the right.
New function: y = |x - 3| - 3 , denoted by function f.
Set a=1. Set b=1.
Set h= 3 which represents the horizontal shift of 3 units to the right.
Set k=- 3 which represents the vertical shift of 3 units down.
Observe the transformation of the absolute value function.
Exercise 9
Perform the following absolute value function transformation:
Vertical stretch by a factor of 3.
New function: y = 3|x| , denoted by function f.
Set a=3. Set b=1.
Set h= 0 since there is no horizontal shift.
Set k= 0 since there is no vertical shift.
Observe the transformation of the absolute value function.
Exercise 8
Perform the following absolute value function transformation:
Vertical shift of 3 units up plus a horizontal shift of 3 units to the left.
New function: y = |x + 3| + 3 , denoted by function f.
Set a=1. Set b=1.
Set h= - 3 which represents the horizontal shift of 3 units to the left.
Set k= 3 which represents the vertical shift of 3 units up.
Observe the transformation of the absolute value function.
Exercise 10
Perform the following absolute value function transformation:
Vertical shrink by a factor of 1/3.
New function: y = 1/3| x| , denoted by function f.
Set a=1/3.
Set b=1.
Set h= - 3 which represents the horizontal shift of 3 units to the left.
Set k= 3 which represents the vertical shift of 3 units up.
Observe the transformation of the absolute value function.
Exercise 11
Perform the following absolute value function transformation:
Horizontal stretch by a factor of 1/3.
New function: y = |1/3x| , denoted by function f.
Set a =1. Set b=1/3.
Set h= 0 since there is no horizontal shift.
Set k= 0 since there is no vertical shift.
Observe the transformation of the absolute value function.
Exercise 12
Perform the following absolute value function transformation:
Horizontal shrink by a factor of 3.
New function: y = |3x| , denoted by function f.
Set a =1. Set b=3.
Set h= 0 since there is no horizontal shift.
Set k= 0 since there is no vertical shift.
Observe the transformation of the absolute value function.
Exercise 13
Perform the following absolute value function transformation:
Vertical shift of 3 units, a horizontal shift of 3 units to the left
and a vertical stretch by a factor of 2.
New function: y = 2|x + 3| + 3 , denoted by function f.
Set a=1. Set b=1.
Set h= - 3 which represents the horizontal shift of 3 units to the left.
Set k= 3 which represents the vertical shift of 3 units up.
Observe the transformation of the absolute value function.
Exercise 14
Perform the following absolute value function transformation:
Vertical shift of 3 units, a horizontal shift of 3 units to the left
and a vertical shrink by a factor of 1/2.
New function: y = 1/2|x + 3| + 3 , denoted by function f.
Set a=1. Set b=1.
Set h= - 3 which represents the horizontal shift of 3 units to the left.
Set k= 3 which represents the vertical shift of 3 units up.
Observe the transformation of the absolute value function.
Exercise 15
Perform the following absolute value function transformation:
Reflection over the x-axis.
New function: y = - |x| , denoted by function f.
Set a=-1. Set b=1.
Set h= 0 since there is no horizontal shift.
Set k= 0 since there is no vertical shift.
Observe the transformation of the absolute value function.
Exercise 16
Perform the following absolute value function transformation:
Reflection over the y-axis.
New function: y = |-x| , denoted by function f.
Set a=1. Set b=-1.
Set h= 0 since there is no horizontal shift.
Set k= 0 since there is no vertical shift.
Observe the transformation of the absolute value function.
Exercise 17
Perform the following absolute value function transformation:
Repeat this exercise as many times as desired until concept is mastered.
Use different values of a, b, h and k.
Exercise 17
Repeat this exercise as many times as desired until concept is mastered.
Use different values of a, b, h and k.