Answer: [tex]\bold{y=7cos\bigg(\dfrac{2\pi}{7}x\bigg)}[/tex]
Step-by-step explanation:
y = A cos (Bx - C) + D
- A = amplitude (vertical stretch)
- Period = 2π/B
- C/B = phase shift
- D = vertical shift
The minimum is -7 and the max is 7 so A = 7 and D = 0
Period is 7. Since P = 2π/B then 7 = 2π/B --> B = 2π/7
Nothing was stated about a phase shift so you can use any value for C. I chose C = 0.
Now, input A = 7, B = 2π/7, C = 0, & D = 0 into the equation
[tex]y=7\cos\bigg(\dfrac{2\pi}{7}x-0\bigg)+0\\\\\\\text{Simplify}:\\y=7\cos\bigg(\dfrac{2\pi}{7}x\bigg)[/tex]
