Question

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Answer 1

`\displaystyle \text{A) }-(2\pi)/(3)`

Explanation:

Trigonometric Functions

Horizontal shifts of trigonometric functions are changes that affect the input axis values and shift the function left or right.

If the function is to be shifted left a units, then the variable x is replaced by x+a and if the function is shifted right a units, then x is replaced by x-a.

The function is:

`y=2\cos\left(x+(2\pi)/(3)\right)+1`

Note the argument of the cosine is
`x+(2\pi)/(3)` which means the value of a is
`-(2\pi)/(3)` and the function is shifted left by
`(2\pi)/(3)`.

Answer:

`\displaystyle \text{A) }-(2\pi)/(3)`