1. **State the problem:** We have a set $A = \{9, 10, 11, 12, 13, 14, 15, 16, 17\}$ and a function $f : A \to \mathbb{N}$ defined by $f(n) = $ the highest prime factor of $n \in A$. We need to write $f$ as a set of ordered pairs and find the range of $f$. 2. **Recall the definition:** The highest prime factor of a number is the largest prime number that divides it exactly. 3. **Find the highest prime factor for each element in $A$:** - $9 = 3^2$, highest prime factor is $3$ - $10 = 2 \times 5$, highest prime factor is $5$ - $11$ is prime, highest prime factor is $11$ - $12 = 2^2 \times 3$, highest prime factor is $3$ - $13$ is prime, highest prime factor is $13$ - $14 = 2 \times 7$, highest prime factor is $7$ - $15 = 3 \times 5$, highest prime factor is $5$ - $16 = 2^4$, highest prime factor is $2$ - $17$ is prime, highest prime factor is $17$ 4. **Write $f$ as a set of ordered pairs:** $$f = \{(9,3), (10,5), (11,11), (12,3), (13,13), (14,7), (15,5), (16,2), (17,17)\}$$ 5. **Find the range of $f$:** The range is the set of all distinct highest prime factors found: $$\text{Range}(f) = \{2, 3, 5, 7, 11, 13, 17\}$$ This completes the problem.