Question

Graph the function by hand using the techniques you were taught in this unit: f(x) = 2sin(x)-2. Your work and explanations must use the methods taught in this class.

• Amplitude: 2

• Period: 2pi

• Midline: y = -2

• y-intercept: (0, -2)

Answer 1

To graph the function f(x) = 2sin(x)-2, we can start by plotting the y-intercept (0, -2).

Next, we can use the amplitude of 2 to mark the highest and lowest points of the graph. The highest point will be 2 units above the midline at y = 0, and the lowest point will be 2 units below the midline at y = -4.

To establish the period of the function, we need to identify the distance between one complete cycle of the graph. Since sine has a period of 2pi, we can see that the period of our function is also 2pi.

Starting from the y-intercept, we can mark a point on the graph that is one-quarter of the way through a cycle, at x = pi/2. The sine function will be at its maximum value of 1 at this point, so the graph will be at y = 0 + 2