key
Which One Doesn’t Belong?
Name:___________________________
Yesterday we learned about the graphs of the parent functions ! = sin ( and ! =
cos (. Today we’ll see how transformations affect these graphs.
1. Give a convincing argument for which of the four graphs doesn’t belong. Can you find a reason
for each of the graphs?
vertical
stretch
A
Amplitude
B
Z
"
.
- -
-
.
,
i
i
.
-
"
'
.
.
C- 2,2 ] instead of
Range
C- I I ]
.
Graph
.
.
is
reflected
there is a min
,
C
"
"
"
i
'
i
is
"
-
"
,
not
-
.
.
..
At X
.
a
-
-
The
Max
.
D
vertical
period
horizontal
shift up
Z
ink
'
Range :
Cl 3 ]
SW
,
A
occurs
complete cycle
IT radians ,
after
The
not zit
graph got compressed
The
.
doesn't go
graph the
Through
origin
.
.
2. The four equations below represent the four graphs. Match each equation with its graph
without the use of a calculator.
shrink )
✓
! = sin(2()
horizontal
compression
C
! = sin(( − +)
phase
B
A
! = 2 sin (
! = sin ( + 2
shift
D
3. Kennedy thinks that the graph of ! = sin(( − +) could also be written as ! = − sin (. Do you
agree or disagree? Explain.
yes
,
if
you
then
you
shift the sine
would have
the
the
right it
graph
down
first
up bump , just like
bump
in
a
reflection
t
.
Section 4.5 Day 2—Transformations of Sine and Cosine
Important Ideas:
Y
=
a-
a
sin
@
(x
c
)
)
td
stretch
vertical
,
y= acosfblx
or
amplitude
horizontal
horizontal
shift / phase shift
Check Your Understanding!
reflection
1. a) Graph ! = −3 cos (
x-axis b)
across
=
ppaerriondof
function
Thorne
.
dilation
factor
+
affects midline
shift ,
D= vertical
a) td
←
Period
shrink it b I
stretch it Ocbc ,
-
lat
=
>
be horizontal
(=
-
range !
✓
!
amplitude
Graph ! = 2 sin( ( − )
"
amplitude =3
right The
=
2
nn
Or
#
midline
2. Determine the domain, range, period, and amplitude of ! = 5 cos 2 (3 + 2
Domain
:
Range
"
IR
:
Period
[ 3.7]
Amplitude
:
y
=
2
s
amps :
41T
:
:
5
3. The equation for the graph below is given by ! = 4 sin(5() + 6. Find the values of A, B, and C.
A-
=
0.5
since
13=1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
c
=
period
still
-
I
21T
since
midline moved
down Innit
4. Which of the following equations is NOT equivalent to the other three?
!
A) ! = cos(( + " )
&
C) ! = sin(( + +)
D) ! = −cos(()
O
o
)
in .× ,
r
"
""
#lxtth ¥5
-- -
B) ! = sin(−()
is
-
osx