Choose the function whose graph is given by?

A. y = sin x + 2

Step-by-step explanation:

Since the graphed function has smooth and even waves, it is a "sinusoidal function" (uses sin or cos). Sinusoidal graphs have an equation of axis, meaning a horizontal line that is the middle of the whole graph. They also have maximum and minimum values, which are the highest and lowest points the graphs reach.

Sinusoidal functions are written in the form:

y = a sin (bx+c) + d or y = a cos (bx+c) + d

a - When negative, indicates a reflection across the x-axis. Vertical stretch/compression. Amplitude.

b - Horizontal stretch or compression.

c - Shift left or right.

d - Shift up or down, which is also the equation of axis.

The middle of the graph, the equation of axis, is x = 2, and d = + 2.

(See the photos below. The order is positive Sine, negative Sine, positive Cosine, negative Cosine.)

(Positive) Sine graphs start at the equation of axis, go upwards to the maximum, then downwards to the minimum and back to the eq. axis. Then repeat.

(Positive) Cosine graphs start at the maximum, go downwards to the minimum and back to the maximum. Then repeat.

Negative Sine graphs still start at the equation of axis, but go downwards then upwards.

Negative Cosine graphs start at the minimum.

The options in the question do not have left/right shifts (if they did, cosine and sine graph can overlap each other). The graph must be a sine graph for starting at the equation of axis. You can see the waves go upwards first, then go down. Therefore the graph is a positive sine graph.

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