Question

Which of the following could be the equation of the function below?

Answer 1

Correct answer is C.

Explanation:

Note that graph in the diagram has period
`\pi.`

Consider the function
`y=-2\cos (2(x+\pi ))-1.`

This function has a period
`T=(2\pi)/(2)=\pi.` Functions in another options have period that differes from
`\pi.`

The graph of this function passes through the point (0,-3), because

`y(0)=-2\cos (2(0+\pi ))-1=-2\cos 2\pi-1=-2\cdot 1-1=-3.`

Answer 2

`y=-2cos (2(x+\pi ))-1`

Explanation:

We are a given a graph from which we can clearly see that y = -1 when x = 0.

Next, we will find out which of the options is the equation of the given graph and for that we need to set our calculator to the radian mode and then put the value of x to be 0.

1. y = -2 cos (4(x + pi)) - 1 = -2 cos (4(0 + pi)) - 1 = 3

2. y = 2 cos(x + pi) = 2 cos(0 + pi) = -1

3. y = -2 cos (2(x + pi)) - 1 = -2 cos (2(x + pi)) - 1 = -3

We get y = -1 when x = 0 in equation number 3, y = -2 cos (2(x + pi)) - 1, so that is the equation of the given graph.