Question

Identify the transformations for the function f(x)=3cos(−x+π3)−2
.(1 point)
Responses

vertical stretch by a factor of 3, horizontal compression by -1, horizontal shift right by π3
, and vertical shift down 2
vertical stretch by a factor of 3, horizontal compression by -1, horizontal shift right by pi over 3, and vertical shift down 2

vertical stretch by a factor of 3, reflection over the y-axis, horizontal shift right by π3
, and vertical shift down 2
vertical stretch by a factor of 3, reflection over the y-axis, horizontal shift right by pi over 3, and vertical shift down 2

vertical stretch by a factor of 3, reflection over the y-axis, horizontal shift left by π3
, and vertical shift down 2
vertical stretch by a factor of 3, reflection over the y-axis, horizontal shift left by pi over 3, and vertical shift down 2

vertical stretch by a factor of 3, reflection over the y-axis, horizontal shift right by π3
, and vertical shift up 2
vertical stretch by a factor of 3, reflection over the y-axis, horizontal shift right by pi over 3, and vertical shift up 2
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Answer 1

Rewrite inside the cosine: -x + π/3 = -(x - π/3), and cos(−θ) = cos θ, so
f(x) = 3 cos(x − π/3) − 2.

Transformations:
- vertical stretch by a factor of 3
- horizontal shift right by π/3
- vertical shift down 2

There is no reflection (the negative inside cancels because cosine is even).