Final answer:
The function y = -3sin(x - π/5) is a transformed sine wave with an amplitude of 3, a horizontal shift of π/5 to the right, and an inversion across the x-axis. Plotting the function involves marking the phase shift, amplitude, and period on the graph, then connecting these points with a sinusoidal curve.
Step-by-step explanation:
To graph the function y = -3sin(x - π/5), one must understand the properties of the sine function and how transformations affect its graph. The coefficient -3 affects the amplitude, the term (x - π/5) translates the graph horizontally, and the negative sign reflects it across the x-axis. The standard sine function has an amplitude of 1, a period of 2π, and no horizontal shift or reflection.
For the given equation, the amplitude is 3, which is the coefficient of the sine function, indicating the graph will oscillate between +3 and -3, not the usual +1 and -1 of the standard sine function.
The phase shift of the function is π/5 to the right since it's in the form of (x - C), where C is positive π/5. The negative sign indicates that the graph of the sine is inverted, producing a reflection across the x-axis.
When graphing the function, start by plotting the phase shift on the x-axis, then mark points where the sine function will cross the x-axis, reach its maximum and minimum values based on the amplitude, and complete one cycle every 2π. Connect these points with a smooth, periodic curve to represent the sinusoidal wave.