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/4
g(x)= cos x

Answer 1

Answer D.

Explanation:

Horizontal stretch by a factor of 4

Answer 2

Option d. Horizontal stretch by a factor of 4.

Explanation:

The given function is:

g(x) = cos(x)

The transformed function is:

f(x) = cos(x/4)

Comparing f(x) with g(x) we can see that in f(x), x is being multiplied by a number "1/4"

Whenever during transformation x is multiplied by a number it indicates horizontal stretch or compression.

• If the number being multiplied is greater than zero, the graph is being compressed horizontally.
• If the number being multiplied to x is lesser than 1, the graph is being stretched in horizontal direction.

In this case 1/4 is being multiplied to x which is smaller than 1, therefore the graph is being stretched in horizontal direction by a factor of 4.

Therefore, the answer to this question is option d. Horizontal stretch by a factor of 4.