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By applying the transformation rules for horizontal and vertical translation, we find that the resulting function is g(x) = cos (x - 7) + 4.

How to find the resulting function by transformation rules

Transformation rules are rules that makes changes on charateristics and behavior of a function to create a new one. Rigid transformations like horizontal and vertical translations are examples of transformation rules. In this question we must apply the following transformation rules to the parent cosine function f(x) = cos x:

  1. Horizontal translation: f'(x) = f(x - 7)      (1)
  2. Vertical translation: g(x) = f'(x) + 4        (2)

Now we proceed to derive the resulting function by applying the rules defined above:

Horizontal translation

f'(x) = cos (x - 7)      (3)

Vertical translation

g(x) = cos (x - 7) + 4     (4)

By applying the transformation rules for horizontal and vertical translation, we find that the resulting function is g(x) = cos (x - 7) + 4.

To learn more on transformation rules: https://brainly.com/question/9201867

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