Question

What are the phase shift and period for the function y = 4cos1/3 (0 + 45) - 3

Phase shift: 45° right, period: 135°
Phase shift: 45° left, period: 120°
Phase shift: 45° right, period: 60°
Phase shift: 45° right, period: 1080°

Answer 1

\[y = 4\cos1/3(\Theta+45) - 3\]

Answer 2

the general form equation is \[\rm y= A \cos (bx+C)+D\]
where
\[\rm \left| A \right|\] is amplitude
phase shift:(horizontal shift: how many units the graph is moving horizontally from the original function ) \[\rm -\frac{ C }{ B }\]
D represent the vertical shift
and you can find period by using the formula \[\rm \frac{ 2\pi }{ \left| B \right| }\]
and if the given value for C is n degree then you can use 360 degree (2pi)

Answer 3

and shifting pattern is same as quadratic equation \[\rm y=a(x-h)^2+k\]
h is horizontal shift and k is vertical shift
if there is negative sign with h then graph shift to the right side
and if it's positive then shift to the left side
or you can set whatever inside the function equal to 0 and then solve for x
\[\rm y=acos(\color{reD}{x- \pi })+d\]\[x- \pi =0\]
solve for x by adding pi both sides
x= pi
so graph shift pi to the right side since x= positive pi