Question

For the function f(x)= -1/2cos(3t+3pi)-3
Identify the amplitude, period, phase shift and vertical Shift

Answer 1

think about the general function \[\cos (t)\]
so what do we know about cosine? that it has an amplitude of 1, that it's period is 2pi
now multiplying by -1/2 to the function makes the amplitude 1/2 but the period still 2pi

now when you subtract 3 from the function cosine you shift it down vertically by 3
then the phase shift is due to the 3t + 3pi so notice you can factor a 3 out so it becomes cos3(t + pi) so the phase shift is by pi to the left and the period is changed to 2pi/3