the function graphed to the right is of the form y = a sin bx or y = a cos bx, where b > 0. determine the…

the function graphed to the right is of the form y = a sin bx or y = a cos bx, where b > 0. determine the equation of the graph. y = □ (type an expression using x as the variable.)

the function graphed to the right is of the form y = a sin bx or y = a cos bx, where b > 0. determine the equation of the graph. y = □ (type an expression using x as the variable.)

Answer

Explanation:

Step1: Determine the amplitude (a)

The amplitude is half the vertical distance between the maximum and minimum values of the function. The maximum value is (2) and the minimum is (- 2). So, (a=\frac{2 - (-2)}{2}=2).

Step2: Determine the period (T)

The period is the horizontal distance between two consecutive peaks or troughs. From the graph, the period (T=\pi).

Step3: Find the value of (b)

The formula for the period of (y = a\sin(bx)) or (y=a\cos(bx)) is (T=\frac{2\pi}{b}). Since (T = \pi), we have (\pi=\frac{2\pi}{b}), solving for (b) gives (b = 2).

Step4: Determine the function type

The graph passes through the origin ((0,0)), so the function is of the form (y=a\sin(bx)) (because (y = a\cos(bx)) has a (y - )intercept of (a) when (x = 0)).

Answer:

(y = 2\sin(2x))