Trigonometric Functions — Test

Question 4 • Algebra II

Which is the graph of y is equal to cosine of x plus 3 ?

Answer

Image with description A coordinate plane. The graph starts and rises to (0 comma 3). It starts to fall through (pi over 2 comma 0) to (pi comma negative 3). It then rises through (3 pi over 2 comma 0) to (2 pi comma 3).

Image with description A coordinate plane. The graph starts and rises to (0 comma 4). It starts to fall through (pi over 2 comma 3) to (pi comma 2). It then rises through (3 pi over 2 comma 3) to (2 pi comma 4).

Image with description A coordinate plane. The graph starts and rises to (0 comma negative 2). It starts to fall through (pi over 2 comma negative 3) to (pi comma negative 4). It then rises through (3 pi over 2 comma negative 3) to (2 pi comma negative 2).

Image with description A coordinate plane. The graph starts and rises to (0 comma 6). It starts to fall through (pi over 2 comma 3) to (pi comma 0). It then rises through (3 pi over 2 comma 3) to (2 pi comma 6).

Explanation

The graph of y = cos x is shifted up 3 units, so add 3 to each cosine value. At x = 0, the height is 1 + 3 = 4; at π/2 it is 0 + 3 = 3; and at π it is −1 + 3 = 2. Choice B has these values and returns to 4 at 2π.

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