Using translation concepts, an horizontal compression of [tex]y = \frac{1}{x}[/tex] by a factor of 6 is given by:
[tex]y = \frac{1}{6x}[/tex]
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the function is given by:
[tex]y = f(x) = \frac{1}{x}[/tex].
A horizontal compression by a factor of 6 is represented by f(6x), hence:
[tex]y = \frac{1}{6x}[/tex]
More can be learned about translation concepts at https://brainly.com/question/4521517
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