Answer:
To graph the function f(x) = 2sin(x) - 2 by hand, we can use the following steps:
Step 1: Find the amplitude
The amplitude of the function is the absolute value of the coefficient of the sine function, which is 2 in this case. Therefore, the amplitude is 2.
Step 2: Find the period
The period of the function is given by the formula 2π/b, where b is the coefficient of x in the sine function. In this case, b = 1, so the period is 2π/1 = 2π.
Step 3: Find the midline
The midline is the horizontal line that the graph oscillates around. For the sine function, the midline is the y-value of the function when there is no vertical shift. In this case, the midline is y = -2.
Step 4: Find the y-intercept
The y-intercept is the value of the function when x = 0. Plugging in x = 0, we get f(0) = 2sin(0) - 2 = -2. Therefore, the y-intercept is -2.
Step 5: Sketch the graph
Based on the amplitude, period, midline, and y-intercept we just found, we can sketch the graph of the function as follows:
- The graph oscillates between y = 2 and y = -6, with a midline at y = -2.
- The graph starts at (0, -2), then goes up to (π/2, 0), down to (π, -2), down further to (3π/2, -4), and back up to (2π, -2).
- The graph is symmetric about the midline.
Therefore, the information about the function is:
Amplitude: 2 (The distance from the midline to the maximum or minimum of the graph is 2.)
Period: 2π (The graph completes one full cycle over a horizontal distance of 2π.)
Midline: y = -2 (The horizontal line that the graph oscillates around.)
y-intercept: -2 (The value of the function when x = 0.)