What is the amplitude, period, and phase shift of f(x) = -3 cos(4x + π) + 6?

Solutions:

f(x) = -3cos(4x + π) +6

The function is in the form: f(x) = λcos( μx - Φ) + β

where, |λ| = amplitude, 2 π/μ = period, Φ/μ = phase shift

So the amplitude is: |-3| = 3

The period is: 2π/4 = π/2

And the phase shift is: -π/4

We may also note that β is the vertical shift of the function and it shift by 6 up or -6 down

What is the amplitude, period, and phase shift of f(x) = -3 cos(4x + π) + 6?

Summary:

The amplitude, period, and phase shift of f(x) = -3 cos(4x + π) + 6 are 3, π/2 and -π/4 respectively.