The function given is fx = 7 sin(4x) + 2. To identify the amplitude, period, and midline, we can analyze the components of the sine function.
Amplitude: The amplitude of a sine function y = a sin(bx) is determined by the absolute value of a. In this case, a = 7. Therefore, the amplitude is 7. This means the graph of the function will oscillate 7 units above and below its midline.
Midline: The midline of a sine function is given by the constant added to the sine component. In this case, it is + 2. Hence, the midline of the function is y = 2. This indicates that the centerline around which the function oscillates is 2 on the y-axis.
Period: The period of a sine function can be calculated using the formula Period = (2π) / b, where b is the coefficient of x. Here, b = 4. Thus, the period is (2π) / 4 = π / 2. This means that the function completes one full cycle in the interval of length π / 2.
To summarize:
- Amplitude: 7
- Period: π / 2
- Midline: y = 2