Answer:
f
(
x
)
=
3
cos
(
2
x
)
+
2
EXPLANATION:
We are able to use the transformation formula
f
(
x
)
=
a
⋅
cos
(
x
−
h
b
)
+
k
. You start with
f
(
x
)
=
cos
(
x
)
and replace
a
with the desired amplitude,
h
with the desired horizontal shift, and
k
with the desired vertical shift. This leaves out the
b
-value. A regular cosine function has a period of
2
π
. If you want a period of
π
, since that is one half of the original period, you need to replace your
b
with a
1
2
.
This is about how it would work out.
f
(
x
)
=
3
⋅
cos
(
x
−
0
1
2
)
+
2
From there you simplify your equation giving you
f
(
x
)
=
3
cos
(
2
x
)
+
2
