the range of y= 2sin(4x)-3
The range is the possible y values for the equation.
Start with the base function. The range of sin(x) is [-1,1].
However, that is multiplied by 2, giving you [-2,2].
The function is shifted down 3, so subtract 3: [-5,-1]
To find the range of the function y = 2sin(4x) - 3, we need to determine the possible values that y can take.
The range of a sine function is [-1, 1], which represents the highest and lowest points on the graph. By multiplying the sine function by 2, we stretch the graph vertically and the range becomes [-2, 2]. Finally, subtracting 3 from the function shifts the graph downwards, so the range now becomes [-2 - 3, 2 - 3], which simplifies to [-5, -1].
Therefore, the range of the function y = 2sin(4x) - 3 is [-5, -1].