What is the range of the trig function sin(-3x+3)?

To find the range of the trigonometric function sin(-3x+3), we need to determine the set of all possible values that the function can produce.

The range of the sine function is from -1 to 1, inclusive. However, since we have an expression inside the sine function, we need to consider how it affects the range.

The expression -3x+3 is a linear function that describes how the input value x is being modified. Since -3x+3 is inside the sine function, it will affect the amplitude and horizontal shift of the graph.

The amplitude of a sine function is the distance between the maximum and minimum values. The general amplitude formula is |A|, where A is the coefficient of x. In this case, the amplitude is |-3| = 3.

The horizontal shift of a sine function is determined by the constant term in the expression. In this case, we have a horizontal shift of 3 units to the right (positive direction).

Combining these findings, we know that the range of the sine function sin(-3x+3) will be from -3 to 3, inclusive, due to the amplitude of 3.

So, the range of the function sin(-3x+3) is [-3, 3].