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)? (3, 7) (2, 7) (5 - π, 7) (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)? (3, 7) (2, 7) (5 - π, 7) (5 + π, 7)

Answer

Answer:

B. (2, 7)

Explanation:

Step1: Find the period of the sinusoidal function

The distance between a maximum and a minimum of a sinusoidal function is half - of the period. The x - values of the maximum (5, 7) and minimum (8, - 2) are 5 and 8 respectively. The difference in x - values is $8 - 5=3$, so the period $T = 6$.

Step2: Determine the x - coordinate of the previous maximum

Since the period is 6, to find the x - coordinate of the maximum immediately preceding the maximum at $x = 5$, we subtract the period from the x - coordinate of the given maximum. So $5-3 = 2$. The y - coordinate of a maximum remains the same for a sinusoidal function of the form $y=a\sin(\pi(x + c))+d$, which is 7. So the coordinates of the previous maximum are (2, 7).