f(x) = 7 sin (4πx) + 3. The function f(x) = 7 sin (4πx) + 3 describe a sinusoidal function whose period is 1/2, maximum value 10, minimum value -4, and it has a y-intercept of 3.
A sinudoidal function whose period is 1/2, maximum value is 10, minimum value is -4, and it has a y-intercept of 3. Let's write to the form f(x) = A sin (ωx +φ) + k, where A is the amplitude, ω is the angular velocity with ω=2πf, (ωx+φ) is the oscillation phase, φ the initial phase (horizontal shift), and k is y-intercept (vertical shift).
Calculating the amplitude:
A = |max - min/2|
A = |10 - (-4)/2| = 14/2
A = 7
calculating the ω:
The period of a sinusoidal is T = 1/f --------> f = 1 / T
ω = 2πf -------> ω = 2π ( 1/T) with T = 1/2
ω = 2π (1/(1/2) = 2π (2)
ω = 4π
The y-intercept k = 3
Writing the equation function with A = 7, ω = 4π, k = 3, φ = 0.
f(x) = A f(x) = A sin (ωx +φ) + k ----------> f(x) = 7 sin (4πx) + 3.
