Question

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

Answer 1

A) Amplitude = 3; period = pi over two; phase shift: x = negative pi over four

Answer 2

This is in the form of
`\sf acos(bx-c)+d`.

Amplitude is equal to
`\sf |a|`
Period is equal to
`\sf(2\pi)/(|b|)`
Phase Shift is equal to
`\sf(c)/(b)`

Plug in the values:

Amplitude:

`\sf |a|\rightarrow |-3|\rightarrow\boxed{\sf 3}`

Period:

`\sf(2\pi)/(|4|)\rightarrow(2\pi)/(4)\rightarrow\boxed{\sf(\pi)/(2)}`

Phase Shift:

`\sf(c)/(b)\rightarrow\boxed{\sf -(\pi)/(4)}`