A translation is a transformation that shifts a graph horizontally or vertically, but doesn’t change the overall shape or orientation.
Example problems on horizontal and vertical translation of absolute value functions
Reflections in the x-axis :
The graph of y = −f(x) is a reflection in the x-axis of the graph of y = f (x).
Note :
Multiplying the outputs by −1 changes their signs.
Reflections in the y-axis :
The graph of y = f(-x) is a reflection in the y-axis of the graph of y = f (x).
Note :
Multiplying the inputs by −1 changes their signs.
Example problems on reflection of absolute value function for a given function
The function which is in the form y = |ax - h| + k
Here a > 1 or 0 < a < 1
The function which is in the form y = a|x - h| + k
Here a > 1 or 0 < a < 1
Describe the
Problem 1 :
y = |x - 2|
Solution :
Comparing the given function with the parent function y = |x|
h = 2, so move the graph 2 units to the right.
Problem 2 :
y = |x|+3
Solution :
Comparing the given function with the parent function y = |x|
h = 3, so move the graph 3 units up.
Problem 3 :
y = 2|x + 3|
Solution :
Comparing the given function with the parent function y = |x|
h = -3, so move the graph 3 units left.
a = 2 > 1 vertical stretch 2 units, so it is narrower.
Problem 4 :
y = 3|x|
Solution :
Comparing the given function with the parent function y = |x|
a = 3 > 1 vertical stretch 3 units, so it is narrower.
Problem 5 :
y = -2|x + 3| - 1
Solution :
Comparing the given function with the parent function y = |x|
Problem 6 :
y = 2|x + 8|
Solution :
Comparing the given function with the parent function y = |x|
Problem 7 :
y = -|x - 6| + 2
Solution :
Comparing the given function with the parent function y = |x|
Problem 8 :
y = (1/2) |x + 2| - 1
Solution :
Comparing the given function with the parent function y = |x|
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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