Question

Which equation(s) can be represented by the graph below?

y = 2sin(3x)
y = 2sin(3x - π/3)
y = 2sin(3x + π/2)
y = 2sin(3x - 2π/3)
A) y = 2sin(3x)
B) y = 2sin(3x - π/3)
C) y = 2sin(3x + π/2)
D) y = 2sin(3x - 2π/3)

Answer 1

C) y = 2sin(3x + π/2). The equation that can be represented by the given graph is y = 2sin(3x + π/2) (option C).

Step-by-step explanation:

The equation that can be represented by the given graph is y = 2sin(3x + π/2) (option C).

Let's analyze the graph: The graph represents a sine function because it oscillates between values of -2 and 2. The amplitude of the function is 2. The period of the function is 2π/3, which means it repeats every 2π/3 units along the x-axis.

To find the equation of the graph, we need to consider the amplitude, phase shift, and period of the function. The amplitude is 2, and the period is 2π/3. The phase shift can be determined by finding the value of x when the function reaches its maximum or minimum. In this case, the maximum occurs at x = 0, so there is no phase shift.