1.What is the amplitude, period, phase shift and vertical shift of the function: f(x) = 3 sin(2x − π) − 1
2.Write a function that is equal to the function:
f(x) = tan (2/3x) − 2
3.Evaluate: sin (2 cos^−1 √2/2)
4.An average seated adult breathes in and out every 4 seconds. The average minimum amount of air in the lungs is 0.08 liter, and the average maximum amount of air in the lungs is 0.82 liter. Suppose the lungs have a minimum amount of air at t = 0, where t is time in seconds.
a. Write a function that models the amount of air in the lungs.
b. Determine the amount of air in the lungs at 5.5 seconds.
1. Amplitude: 3, Period: π/2, Phase Shift: π, Vertical Shift: -1
2. f(x) = tan (2/3x) - 2
3. sin (2 cos^−1 √2/2) = 1
4a. f(x) = 0.37sin(π/2x - π) + 0.42
4b. f(5.5) = 0.37sin(2.75π - π) + 0.42 = 0.37sin(1.75π) + 0.42 = 0.37(1) + 0.42 = 0.79