Determine the minimum and maximum value of the following trigonometric function.f, of, x, equals, minus, 3, sine, x, plus, 1f(x)=−3sinx+1

The function given is f(x) = -3sin(x) + 1.

Step 1: Identify the amplitude of the function The amplitude of the function is the absolute value of the coefficient of the sine function, which is |-3| = 3.

Step 2: Identify the vertical shift of the function The vertical shift of the function is the constant term, which is +1.

Step 3: Determine the minimum and maximum values The minimum and maximum values of a sine function occur at the peak and trough of its wave, respectively. Since the amplitude of the function is 3, the wave of the function goes 3 units up and 3 units down from its vertical shift.

Therefore, the minimum value of the function is 1 - 3 = -2 and the maximum value of the function is 1 + 3 = 4.