Question

In as much detail as possible, explain how you would graph the equation y = 3sin(1/2(x 1)) + 5.

Answer 1

To graph the equation y = 3sin(1/2(x + 1)) + 5, identify the amplitude, period, and phase shift, determine the x-values that span one period, plot the points, and connect them.

Step-by-step explanation:

To graph the equation y = 3sin(1/2(x + 1)) + 5, we can follow these steps:

1. Identify the amplitude, period, and phase shift of the sine function.
2. Determine the values of x that span one period of the graph.
3. Plot the points by substituting the x-values into the equation and calculating the corresponding y-values.
4. Connect the points with a smooth curve to complete the graph.

The amplitude of the sine function is 3, which determines the maximum and minimum values of y. The period is 2π/1/2 = 4π, and the phase shift is -1, indicating that the graph is shifted 1 unit to the left. To plot the points, we can choose x-values that cover one period, such as x = -3π, -2π, -π, 0, π, 2π, 3π. Substituting these values into the equation gives us the corresponding y-values. Finally, we can connect the points to create a smooth curve.