state the range of y=2sin(4x)-3
remember the range of
y = sin(x) is between -1 and +1
so the range of y = 2sin(4x) is between -2 and +2
(the angle of 4x has no effect in the vertical direction of the graph, it affects only the frequency)
then the entire graph is dropped 3 units, so the range of y = 2sin(4x) - 3 is
-5 ≤ y ≤ -1
To find the range of the function y = 2sin(4x) - 3, we need to determine the possible values y can take.
The range of a sinusoidal function can be determined by looking at the amplitude and the vertical shift.
The amplitude of the function is the coefficient of the sine term, which is 2 in this case. The amplitude represents the maximum value of the function above and below its midline. Since the sine function oscillates between -1 and 1, the amplitude of 2 scales this range. So, the maximum value of y is 2 and the minimum value is -2.
The vertical shift of the function is the constant term at the end, which is -3. This shifts the entire graph vertically downward by 3 units. Therefore, the maximum value of y becomes 2 - 3 = -1 and the minimum value becomes -2 - 3 = -5.
Combining these values, we conclude that the range of y = 2sin(4x) - 3 is between -5 and -1.