Question

What is the equation of the graph below?

Answer 1

Answer: Choice D
y = cos(x+pi)

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Explanation:

Make sure your calculator is in radian mode. 
If we plug x = 0 into each answer choice, we get the following
Choice A: y = cos(x+pi/2) = cos(0+pi/2) = 0
Choice B: y = cos(x+2pi) = cos(0+2pi) = 1
Choice C: y = cos(x+pi/3) = cos(0+pi/3) = 1/2 = 0.5
Choice D: y = cos(x+pi) = cos(0+pi) = -1

Only choice D has x = 0 lead to y = -1.
Therefore (0,-1) is a point on the equation of choice D. The graph shows this visually through the y intercept, where the graph crosses the y axis.