Question

Choose the graph of y = 2 cos x

Answer 1

y = cos x begins at (0,1), descends to (pi/2,0), descends to (pi,-1), ascends to (3pi/2,0), and then ascends to (2pi,1). This covers only one full period.

The graph of y = 2cost x is the same, except that the amplitudes (y-values) are 2x as great as before:

(0,2), (pi/2, 0), and so on.

Answer 2

The graph is in the attachment.

Explanation:

The cosine function is periodic. This means that every 2pi, the image is the same.

For y = 2 cos x, the amplitude of the function is given by 2.

The domain of the function is (-∞,∞).

The image of the function is [-2, 2].

For example:

y(0) = 2 cos 0 = 2 . 1 = 2.

y(pi/2) = 2 cos(pi/2) = 2 * 0 = 0.

y(pi) = 2 cos(pi) = 2 * -1 = -2.

y(3pi/2) = 2 cos(3pi/2) = 2 * 0 = 0.

y(2pi) = 2 cos(2pi) = 2 * 1 = 2.