Answer:
The equation of the graph below is:
[tex]y=\cos (x+\pi)[/tex]
Step-by-step explanation:
Clearly from the graph that is provided to us we observe that when x=0 the value of the cosine function is: -1
Hence, we put x=0 in each of the given options and check which hold true.
A)
[tex]y=\cos (x+\dfrac{\pi}{2})[/tex]
when x=0 we have:
[tex]y=\cos (\dfrac{\pi}{2})\\\\\\y=0\neq -1[/tex]
Hence, option: A is incorrect.
B)
[tex]y=\cos (x+2\pi)[/tex]
when x=0 we have:
[tex]y=\cos (2\pi)\\\\\\y=1\neq -1[/tex]
Hence, option: B is incorrect.
C)
[tex]y=\cos (x+\dfrac{\pi}{3})[/tex]
when x=0 we have:
[tex]y=\cos (\dfrac{\pi}{3})\\\\\\y=\dfrac{1}{2}\neq -1[/tex]
Hence, option: C is incorrect.
D)
[tex]y=\cos (x+\pi)[/tex]
when x=0 we have:
[tex]y=\cos (\pi)\\\\\\y=-1[/tex]
Similarly by the graph of the function we see that it matches the given graph.
Hence, option: D is correct.
