Question

Which of the following is the graph of y = cosine (2 (x + pi))?

On a coordinate plane, a curve crosses the y-axis at (0, negative 1). It has a minimum of negative 1 and a maximum of 1. It goes through 2 cycles at pi.
On a coordinate plane, a curve crosses the y-axis at (0, negative 1). It has a minimum of negative 1 and a maximum of 1. It goes through 1 cycle at pi.
On a coordinate plane, a curve crosses the y-axis at (0, 1). It has a minimum of negative 1 and a maximum of 1. It goes through 1 cycle at 4 pi.
On a coordinate plane, a curve crosses the y-axis at (0, 1). It has a minimum of negative 1 and a maximum of 1. It goes through 2 cycles at 2 pi.

Answer 1

The graph of y = cosine (2 (x + pi)) crosses the y-axis at (0,1), has a maximum of 1 and a minimum of -1, and completes 2 cycles in the interval from 0 to 2π.

Step-by-step explanation:

The graph of the function y = cosine (2 (x + pi)) can be determined by analyzing its properties and comparing them with the given options. The cosine function oscillates between +1 and -1, which means the amplitude of this function is 1. The presence of a '2' within the cosine function indicates that the function's period is π rather than the standard 2π period of a regular cosine function, since the period of cosine is π / b, where b is the coefficient of x, which in this case is 2. Additionally, the horizontal shift of the function is -π, which is a phase shift to the right. Given these details, the graph should cross the y-axis at (0,1) because cosine of 0 is 1, have a minimum of -1 and a maximum of 1, and complete two cycles between 0 and 2π, since the period is π and thus there would be two repetitions in a span of 2π.

Answer 2

D

Step-by-step explanation:

Because i said so.