Answer:
![f(x)= \sin(6x)+3](https://tex.z-dn.net/?f=f%28x%29%3D%20%5Csin%286x%29%2B3)
Step-by-step explanation:
The parent function of this graph is: y = sin(x)
The sine function is periodic, meaning it repeats forever.
Standard form of a sine function:
![f(x) = \sf A \sin (B(x + C)) + D](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Csf%20A%20%5Csin%20%28B%28x%20%2B%20C%29%29%20%2B%20D)
- A = amplitude (height from the mid-line to the peak)
- 2π/B = period (horizontal distance between consecutive peaks)
- C = phase shift (horizontal shift - positive is to the left)
- D = vertical shift
The parent function y = sin(x) has the following:
- Amplitude (A) = 1
- Period = 2π
- Phase shift (C) = 0
- Vertical shift (D) = 0
- Mid-line: y = 0
From inspection of the given graph:
- Amplitude (A) = 1
![\sf Period=\dfrac{\pi}{12}-\dfrac{-\pi}{4}=\dfrac{\pi}{3}](https://tex.z-dn.net/?f=%5Csf%20Period%3D%5Cdfrac%7B%5Cpi%7D%7B12%7D-%5Cdfrac%7B-%5Cpi%7D%7B4%7D%3D%5Cdfrac%7B%5Cpi%7D%7B3%7D)
- Phase shift (C) = 0
- Vertical shift (D) = +3 (as mid-line is y = 3)
![\sf If\:Period=\dfrac{\pi}{3} \implies \dfrac{2 \pi}{B}=\dfrac{\pi}{3}\implies B=6](https://tex.z-dn.net/?f=%5Csf%20If%5C%3APeriod%3D%5Cdfrac%7B%5Cpi%7D%7B3%7D%20%5Cimplies%20%5Cdfrac%7B2%20%5Cpi%7D%7BB%7D%3D%5Cdfrac%7B%5Cpi%7D%7B3%7D%5Cimplies%20B%3D6)
Substituting the values into the standard form:
![\implies f(x) =1 \sin (6(x + 0)) + 3](https://tex.z-dn.net/?f=%5Cimplies%20f%28x%29%20%3D1%20%5Csin%20%286%28x%20%2B%200%29%29%20%2B%203)
![\implies f(x) = \sin (6x) + 3](https://tex.z-dn.net/?f=%5Cimplies%20f%28x%29%20%3D%20%5Csin%20%286x%29%20%2B%203)
Therefore, the equation of the given trigonometric graph is:
![f(x)= \sin(6x)+3](https://tex.z-dn.net/?f=f%28x%29%3D%20%5Csin%286x%29%2B3)
Answer:
17
Step-by-step explanation:
8*2=4
4+8+5= 17