To determine if the given set of points forms a function, we need to check whether each input $x$-value (domain) maps to exactly one output $y$-value (range). In other words, no $x$-value can have more than one corresponding $y$-value.

The points are: $(8,2), (4,3), (1,7), (2,9), (0,5)$

Steps:

1. Extract the $x$-values (inputs): $8, 4, 1, 2, 0$.
2. Check if any $x$-value repeats. If it does, it must map to the same $y$-value for the set to still be a function.

Observation:

• The $x$-values $8, 4, 1, 2, 0$ are all unique, and there are no repeated $x$-values. Each $x$-value corresponds to exactly one $y$-value.

Conclusion:

Yes, the given set of points represents a function, because each $x$-value has a unique $y$-value.

Would you like further clarification or an example with non-functions?

Here are 5 related questions for deeper understanding:

1. How can you determine if a graph represents a function using the vertical line test?
2. What happens if an $x$-value repeats in a set of points?
3. How can we determine the domain and range of this function?
4. Are all functions one-to-one? Why or why not?
5. Can a function have the same $y$-value for different $x$-values?

Tip: A quick way to check if a set of points is a function is to see if any $x$-values repeat!