Question

Mason stands on the
\[5^\text{th}\] step of a vertical ladder. The ladder has
\[15\] steps, and the height difference between consecutive steps is
\[0.5\text{ m}\].
\[h(n)\] models the height above the ground of Mason's feet (in
\[\text{m}\]) after moving
\[n\] steps (if Mason went down the ladder,
\[n\] is negative.)
What's the appropriate domain?

Answer 1

Mason can move only an integer number of steps and must stay on steps 1 through 15. Starting on step 5, the final step is 5 + n, so

1 ≤ 5 + n ≤ 15 ⇒ −4 ≤ n ≤ 10.

Thus the domain is the integers n with −4 ≤ n ≤ 10, i.e. {−4, −3, …, 10}.