Final answer:
To graph the function f(x) = 2sin(x)-2 by hand, start by understanding the properties of the sin(x) function and then use a set of x-values to calculate corresponding y-values and plot the points.
Step-by-step explanation:
To graph the function f(x) = 2sin(x)-2 by hand, we can start by understanding what the function represents. The sin(x) function is a periodic function that oscillates between -1 and 1 every 2 radians. By multiplying it by 2 and subtracting 2, we are scaling the function vertically and shifting it downward by 2 units.
To plot the graph, we can choose a set of x-values, calculate the corresponding y-values using the function, and then plot the points. We can repeat this process for multiple x-values, which will give us a smooth curve representing the function.
For example, if we choose a few x-values such as 0, π/2, π, 3π/2, and 2π, we can calculate the corresponding y-values and plot the points. Connecting these points with a smooth curve will give us the graph of the function f(x) = 2sin(x)-2.