the sinusoidal function f(x)=a sin(π(x + c))+d, where a, c, and d are real numbers, has a maximum at the…

the sinusoidal function f(x)=a sin(π(x + c))+d, where a, c, and d are real numbers, has a maximum at the ordered pair (5, 7) and a minimum at the ordered pair (8, -2). which of the following could be the coordinates of the maximum immediately preceding (5, 7)?\no (3, 7)\no (2, 7)\no (5 - π, 7)\no (5 + π, 7)

the sinusoidal function f(x)=a sin(π(x + c))+d, where a, c, and d are real numbers, has a maximum at the ordered pair (5, 7) and a minimum at the ordered pair (8, -2). which of the following could be the coordinates of the maximum immediately preceding (5, 7)?\no (3, 7)\no (2, 7)\no (5 - π, 7)\no (5 + π, 7)

Answer

Answer:

A. (2, 7)

Explanation:

Step1: Find the period of the function

The distance between a maximum and a minimum of a sinusoidal function $y = a\sin(b(x + c))+d$ is half - period. Given a maximum at $(5,7)$ and a minimum at $(8, - 2)$, the horizontal distance between them is $x_2 - x_1=8 - 5 = 3$. So, $\frac{T}{2}=3$, then the period $T = 6$.

Step2: Determine the previous maximum

The maximum values of a sinusoidal function occur at intervals of one period. To find the maximum immediately preceding $(5,7)$, we subtract the period divided by 2 from the x - coordinate of the given maximum. Since the period $T = 6$, subtracting 3 from the x - coordinate of the point $(5,7)$ gives us the point $(5-3,7)=(2,7)$.