Answer:
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."
