Question

Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x).
f(x) = cos (x/6) ; g(x) = cos x

Horizontal stretch by a factor of 6

Vertical stretch by a factor of 6

Vertical shrink by a factor 1/6

Horizontal shrink by a factor 1/6

Answer 1

Acos(Bx + C) + D

B = changes the original period of \(2\pi\) to \(\bf \cfrac{2\pi}{B} \), thus stretching it or shrinking it
$$\bf
f(x)= cos\left(\frac{x}{6}\right) \implies f(x)= cos\left(\frac{1}{6}x\right)
$$