This document contains a lesson on graphing transformations of the parent function y=x. It includes examples of transformations involving reflection (y=-x), vertical shifts (y=x+k), horizontal shifts (y=x-h), stretching/shrinking (y=ax), and combinations. The key effects of each transformation type are explained. Students are asked to graph examples, identify domains/ranges, intercepts, and describe the transformations. The last section introduces the concept of end behavior and compares it between parabolas and square root graphs.

1. FoCCM2
Lesson
4
Name
___________________________
Unit
3
–
Radicals
Period
_______
Date
_____________
1
1.
Parent
Graph:
𝑦 = 𝑥
Answer
the
following
questions
about
the
parent
graph
𝑦 = 𝑥
,
if
none
exists
write
none.
a)
Domain
for
𝑦 = 𝑥
is
________________________________________
b)
Range
for
𝑦 = 𝑥
is
__________________________________________
c)
y-­‐intercept(s)
is
____________________________________________
d)
x-­‐intercept(s)
is
___________________________________________
TRANSFORMATIONS
of
𝒚 = 𝒙
Explain
by
using
words
like
left/right,
up/down,
reflected
over,
vertical
stretch,
and
vertical
shrink
Using
your
graphing
calculator
sketch
each
graph
and
determine
how
each
graph
has
shifted
or
changed
shape:
2.
𝑦 = − 𝑥
a)
Explain
transformation
of
the
parent
graph
𝑦 = 𝑥
___________________________________________________________
b)
Domain
______________________
Range____________________
c)
y-­‐intercept(s)
_________________
x-­‐intercept(s)
______________
c)
Describe
the
changes,
if
there
are
any,
in
domain,
range,
y-­‐intercepts,
and
x-­‐intercepts
x
y
-­‐9
-­‐4
-­‐1
0
1
4
9

2. FoCCM2
Lesson
4
Name
___________________________
Unit
3
–
Radicals
Period
_______
Date
_____________
2
3.
𝑦 = 𝑥 + 3
𝑦 = 𝑥 − 5
𝑦 = − 𝑥 + 2
a)
Explain
transformation
of
the
parent
graph
𝑦 = 𝑥
to
𝑦 = 𝑥 + 𝑘,
how
does
the
k
effect
the
graph?
______________________________________________________________________________________________________
b)
Domain
______________________
Range____________________
c)
y-­‐intercept(s)
_________________
x-­‐intercept(s)
______________
c)
Describe
the
changes,
if
there
are
any,
in
domain,
range,
y-­‐intercepts,
and
x-­‐intercepts
d)
What
transformations
were
applied
in
the
last
graph?
4.
𝑦 = 𝑥 − 4
𝑦 = 𝑥 + 5
𝑦 = 𝑥 − 6 + 2
a)
Explain
transformation
of
the
parent
graph
𝑦 = 𝑥
to
𝑦 = 𝑥 − ℎ,
how
does
the
h
effect
the
graph?
______________________________________________________________________________________________________

3. FoCCM2
Lesson
4
Name
___________________________
Unit
3
–
Radicals
Period
_______
Date
_____________
3
b)
Domain
______________________
Range____________________
c)
y-­‐intercept(s)
_________________
x-­‐intercept(s)
______________
c)
Describe
the
changes,
if
there
are
any,
in
domain,
range,
y-­‐intercepts,
and
x-­‐intercepts
d)
What
transformations
were
applied
in
the
last
graph?
5.
𝑦 = 3 𝑥
𝑦 =
!
!
𝑥
𝑦 = −2 𝑥 − 5
a)
Explain
transformation
of
the
parent
graph
𝑦 = 𝑥
to
𝑦 = 𝑎 𝑥,
how
does
the
a
effect
the
graph?
______________________________________________________________________________________________________
b)
Domain
______________________
Range____________________
c)
y-­‐intercept(s)
_________________
x-­‐intercept(s)
______________
c)
Describe
the
changes,
if
there
are
any,
in
domain,
range,
y-­‐intercepts,
and
x-­‐intercepts
d)
What
transformations
were
applied
in
the
last
graph?
Summary:
Given:
𝑦 = 𝑎 𝑥 − ℎ + 𝑘
Explain
the
change
to
the
parent
graph
𝑦 = 𝑥
for
each:
if
0 < 𝑎 < 1
,
then
vertical
stretch
or
shrink
(circle
one)
if
𝑎 > 0
,
then
vertical
stretch
or
shrink
(circle
one)
if
𝑥 − ℎ,
then
shift
right
or
left
(circle
one)
if
𝑥 + ℎ,
then
shift
right
or
left
(circle
one)
if
𝑥 + 𝑘,
then
shift
up
or
down
(circle
one)
if
𝑥 − 𝑘,
then
shift
up
or
down
(circle
one)

4. FoCCM2
Lesson
4
Name
___________________________
Unit
3
–
Radicals
Period
_______
Date
_____________
4
Lesson
5
1. What
is
“end
behavior?”
a) What
Happens
at
the
Ends?
As
you
move
farther
and
farther
away
from
zero,
what
does
the
graph
look
like?
• Follow
the
graph
to
very
large
values
of
x,
(right-­‐
positive
x
values)
• Follow
the
graph
to
very
small
values
of
x,
(left-­‐
negative
x
values)
2. How
is
the
end
behavior
for
the
parabola
different
or
the
same
for
the
square
root
graph?
Ex.
End
Behavior:
End
Behavior:
As
the
value
for
x
gets
larger
.
.
.
As
the
value
for
x
gets
smaller
.
.
.
_____________________________________
_____________________________________
End
Behavior:
End
Behavior:
As
the
value
for
x
gets
larger
.
.
.
As
the
value
for
x
gets
smaller
.
.
.
_____________________________________
_____________________________________