Which of the following could be the equation of the function below?

On a coordinate plane, a curve crosses the y-axis at y = negative 1.5. It has a maximum at negative 1.5 and a minimum at negative 2.5. It goes through 2 cycles at pi.

y = 0.5 cosine (2 (x minus StartFraction pi Over 2 EndFraction)) + 2

y = 0.5 cosine (4 (x minus StartFraction pi Over 2 EndFraction)) minus 2

y = 0.5 cosine (4 (x + pi)) + 2

y = 0.5 cosine (2 (x minus pi)) minus 2

y = 0.5 cosine (4 (x - pi/2)) - 2

Step-by-step explanation:

Taking the general form:

y = A cosine (Bx - Cπ)) + D

In the following case. the constants are:

y = 0.5 cosine (4x - 2π)) - 2

A: 0.5

B: 4

C: 2π

D: - 2

The range of this function is:

range = [-|A|+D, |A|+D]

range = [-0.5-2, 0.5-2]

range = [-2.5, - 1.5]

Which coincides with "It has a maximum at negative 1.5 and a minimum at negative 2.5"

At x = 0, the function value is:

y = 0.5 cosine (4 (0) - 2π)) - 2

y = 0.5 - 2 = - 1.5

As indicated in "a curve crosses the y-axis at y = negative 1.5"

The period of the function is:

period: 2π/B

period = 2π/4 = π/2 or 2 cycles at π

as described in "It goes through 2 cycles at pi."