What is the amplitude, period, and phase shift of f(x) = −3 cos(4x + π) + 6?
This is in the form of \(\sf acos(bx-c)+d\).
Amplitude is equal to \(\sf |a|\)
Period is equal to \(\sf\dfrac{2\pi}{|b|}\)
Phase Shift is equal to \(\sf\dfrac{c}{b}\)
Plug in the values:
Amplitude:
\(\sf |a|\rightarrow |-3|\rightarrow\boxed{\sf 3}\)
Period:
\(\sf\dfrac{2\pi}{|4|}\rightarrow\dfrac{2\pi}{4}\rightarrow\boxed{\sf\dfrac{\pi}{2}}\)
Phase Shift:
\(\sf\dfrac{c}{b}\rightarrow\boxed{\sf -\dfrac{\pi}{4}}\)
Answer:
A) Amplitude = 3; period = pi over two; phase shift: x = negative pi over four