Unit 1, Day 9 - Rigid
Transformations
We will review rigid transformations of
the basic parent functions
and
I will graph these transformations.
September 2, 2016
Vertical Shifts

Set your viewing window to [-5, 5] by [-5, 15]
and graph the following functions:
 Y1
= x2
 Y2 = x2 + 3
 Y3 = x2 +1
 Y4 = x2 – 2
 Y5 = x2 – 4


What do the +3, +1, -2, and -4 seem to do?
Repeat this for x3, |x|, and √x. Are the results the
same?
Vertical Translations
y = f(x) + k
translation up by k units
y = f(x) – k
translation down by k
units
Horizontal Shifts

Set your viewing window to [-5, 5] by [-5, 15]
and graph the following functions:
 Y1
= x2
 Y2 = (x + 3)2
 Y3 = (x +1)2
 Y4 = (x – 2)2
 Y5 = (x – 4)2


What do the +3, +1, -2, and -4 seem to do?
Repeat this for x3, |x|, and √x. Are the results the
same?
Horizontal Translations
y = f(x - h)
translation right by h
units
y = f(x + h)
translation left by h
units
Give the equation to each graph.
y = |x| - 4
y = |x – 2|
Write the function whose graph is the graph of y =
x3, but is shifted to the right 4 units.
y = (x – 4)3
Reflections
•
•
•
•
Graph
• Y1 = √x
• Y2 = -√x
What do you observe?
A reflection across the x-axis occurs when y
is replaced by –y
y = -f(x)
Reflection across the x-axis
Write the equation for each graph.
y = -x2
y = -x2 + 2
y = -(x + 2)2
Reflections
•
•
•
•
Graph
• Y1 = √x
• Y2 = √-x
What do you observe?
A reflection across the y-axis occurs when x
is replaced by –x
y = f(-x)
Reflection across the y-axis
Example: Graph each function using shifting and/or
reflecting. Start with the graph of the basic
function (for example, y = x2) and show all stages.
a) f(x) = (x – 1)3 + 2
b) f(x) = -(x + 1)2 - 1
Rigid Transformations (flipbook)
Transformation
“Formula”
What it does
Example using
f(x) = x2
Vertical Shifts
y = f(x) + k
Translation up by
k units
y = x2 + 2
y = f(x) – k
Translation down
by k units
y = x2 - 2
y = f(x – h)
Translation right by
h units
y = (x – 2)2
y = f(x + h)
Translation left by h
units
y = (x + 2)2
y = -f(x)
Reflection across
the x-axis
y = -x2
y = f(-x)
Reflection across
the y-axis
y = (-x)2
Horizontal Shifts
Reflections