Question

Simonne has been following the stock ratings of Carter's Pork Bellies. She has noticed that the pattern can be modeled by a cosine function. During her observations, she has found the stock to have a maximum of x = 6, minimum of x = −2, and period of π. Which of the following cosine functions could model Simonne's stock rating?

a. f(x) = 4 cos 2x − 4

b. f(x) = 6 cos pi over 2 x + 2

c. f(x) = 6 cos pi over 2 x − 4

d. f(x) = 4 cos 2x + 2

Answer 1

y=a cos (bx+c) + d
Maximun: M=6
Minimum: m=-2
Period: P=π

d=(M+m)/2
d=(6+(-2))/2
d=(6-2)/2
d=4/2
d=2

P=2π/b
π=2π/b
Sollving for b. Cross multiplication:
πb=2π
Dividing both sides by π:
πb/π=2π/π
b=2

Amplitude=a=(M-m)/2
a=(6-(-2))/2
a=(6+2)/2
a=8/2
a=4

y=4 cos (2x+0) + 2
y=4 cos 2x +2

Answer: Option d. f(x) = 4 cos 2x + 2