The function given is fx = 5 sin(x) + 3.
Amplitude:
The amplitude of a sine function is determined by the coefficient in front of the sine. In this case, the coefficient is 5. This means the amplitude is 5. The amplitude represents how far the graph of the function stretches vertically from its midline.
Period:
The period of a sine function is calculated using the formula 2π / |b|, where b is the coefficient of x in the function. Here, since the function is 5 sin(x), the value of b is 1. Thus, the period of this function is:
Period = 2π / |1| = 2π.
Midline:
The midline of the function is determined by the vertical shift. In this case, the function is shifted up by 3 units because of the +3. Therefore, the midline is:
y = 3.
In summary:
- Amplitude: 5
- Period: 2π
- Midline: y = 3