The correct option is A. a customer will earn 1 free night per 10 night stayed.
Given,
[tex]f(x)=\dfrac{x}{10}[/tex]..........equation (1) .
Since the hotel offers a reward program based on the number of nights stayed. The function [tex]f(x)[/tex] represents the number of free nights earned as a function of [tex]x[/tex], the number of nights stayed.
From equation (1), it is clear that f(x) is the one- tenth times of x. it means the customer will earn 1 free night per 10 night stayed.
Hence the correct option is A. a customer will earn 1 free night per 10 night stayed.
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