Question

check my answer? amplitude, period, phase shift and midline question


What are the amplitude, period, phase shift, and midline of f(x) = −3 sin(4x − π) + 2? (6 points)
Amplitude: 3; period: pi over 2 ; phase shift: x = pi over 4 ; midline: y = 2
Amplitude: −3; period: pi over 2 ; phase shift: x = pi over 2 ; midline: y = 2
Amplitude: 2; period: pi over 4 ; phase shift: x = pi over 4 ; midline: y = −3
Amplitude: 2; period: pi over 4 ; phase shift: x = pi over 2 ; midline: y = −3

i believe it is Amplitude: −3; period: pi over 2 ; phase shift: x = pi over 2 ; midline: y = 2

Answer 1

the period and phase shift part is throwing me off

Answer 2

re-writing \( f(x) = -3 \sin (4 x - \pi) + 2\)

as

\( f(x) = -3 \sin 4 (x - \dfrac{\pi}{4}) + 2\)

might help you


and as an example, for \(y(x) = \sin \omega ( x - \phi) + y_o\)

- the period is \(T = \dfrac{2 \pi}{\omega} \) and

- the phase shift is \(\phi\)

Answer 3

@irishboy123 thank you very much!! this helped a lot!!