a hotel offers a reward program based on the number of nights stayed. the function f(x) represents the…
a hotel offers a reward program based on the number of nights stayed. the function f(x) represents the number of free nights earned as a function of x, the number of nights stayed.\n\nf(x) = ⌊x/10⌋\n\nwhich describes the meaning of f(x)?\n\na customer earns 1 free night per 10 nights stayed.\na customer starts with 1 free night and then earns another free night after every 10 nights stayed.\na customer earns x - 10 free nights for every 10 nights stayed.\na customer earns 10 free nights after x number of nights stayed.
Answer
Explanation:
Step1: Analyze the function
The function $f(x)=\lfloor\frac{x}{10}\rfloor$. The floor - function $\lfloor y\rfloor$ gives the greatest integer less than or equal to $y$. Here, when we divide the number of nights stayed $x$ by 10, $\frac{x}{10}$ represents the ratio of the number of nights stayed to 10. Taking the floor of this ratio means we are counting the number of full - sets of 10 nights in $x$ nights.
Step2: Interpret the result
For every 10 nights a customer stays, they earn 1 free night. For example, if $x = 10$, then $f(10)=\lfloor\frac{10}{10}\rfloor=\lfloor1\rfloor = 1$ (1 free night for 10 nights stayed); if $x = 20$, then $f(20)=\lfloor\frac{20}{10}\rfloor=\lfloor2\rfloor = 2$ (2 free nights for 20 nights stayed).
Answer:
A. A customer earns 1 free night per 10 nights stayed.