Answer:
Third option: The graph moves left 18 units.
Step-by-step explanation:
Some transformations for a function f(x) are shown below:
If , the function is shifted up "k" units.
If , the function is shifted down "k" units.
If , the function is shifted left "k" units.
If , the function is shifted right "k" units.
In this case, we can observe that graph of is changed to
Since:
We can conclude that the function is shifted left 18 units to get the function
.
Since the beacons rotate together, the angular speed is constant.
From the time you see the first beacon, you have to wait for the lighthouse to make 120°, i.e. 1/3 of a whole turn.
So, if T is the time it takes for the lighthouse to make a whole turn, the interval between the first and the second beacon is T/3.
The interval between the second and third beacon is the amount of time it takes to the lighthouse to make the remaining 2/3 of a turn, so that you'll see the first beacon again. So, this time is 2T/3
So, the ratio is
So, the time between the second and third beacon is twice as much the time between the first two.