(10.04 MC) What cosine function represents an amplitude of 3, a period of π, no horizontal shift, and a vertical shift of 2? (6 points)

Group of answer choices

f(x) = 3 cos 2x + 2

f(x) = 3 cos πx + 2

f(x) = 2 cos πx + 3

f(x) = 2 cos 2x + 3

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

-232

step-by-step explanation:

14

step-by-step explanation:

14 x 3 = 42