Step-by-step explanation:
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1. Determine the period of the function: The period of the sine function is 2π. Since the coefficient in front of the x is 1, the period of the function g(x) = 3sin(x) is also 2π.
2. Determine the amplitude of the function: The amplitude of the sine function is 1. The amplitude of the function g(x) = 3sin(x) is 3, since the coefficient in front of the sin(x) is 3.
3. Determine the phase shift of the function: Since there is no term inside the sin function in g(x) = 3sin(x), the phase shift is 0.
4. Plot the key points: Since the period is 2π, we will plot the points at x = 0, x = [tex]\frac{π}{2}[/tex], x = π, x = [tex]\frac{3π}{2}[/tex], and x = 2π.
5. Calculate the y-values for each of these points: Since g(x) = 3sin(x), we can calculate the y-values by evaluating the sin function at each x-value and multiplying by 3.
6. Plot the points on the graph and connect them with a smooth curve: Once you have calculated the y-values, plot the points on the graph and connect them with a smooth curve.
7. Extend the graph: Since the sine function repeats every 2π, you can extend the graph by repeating the pattern in each period.
Following these steps will help you graph the function g(x) = 3sin(x) accurately.