Question

Mason stands on the 5th step of a vertical ladder. The ladder has 15 steps, and the height difference between consecutive steps is 0.5 m. h(n) models the height above the ground of Mason's feet (in m) after moving n steps (if Mason went down the ladder, n is negative.) Which number type is more appropriate for the domain of h?

A) Integers

B) Real numbers

What's the appropriate domain?

A) −5≤n≤10

B) −2.5≤n≤5

C) 0≤n≤7.5

Answer 1

The appropriate number type for the domain of the height function h is integers, and the correct domain is -5≤n≤10, as each step is 0.5 m and Mason can move up or down the ladder.

Step-by-step explanation:

The student is working on a problem involving a vertical ladder with 15 steps, with Mason initially standing on the 5th step. Given that the height difference between consecutive steps is 0.5 m, the function h(n) models Mason's height above the ground after moving n steps. To determine the appropriate domain of h, we need to consider that n could be positive or negative depending on whether Mason moves up or down the ladder.

Since each step is 0.5 m, we only consider n as whole numbers, and thus n should belong to the set of integers, not real numbers. When n is 0, Mason has not moved from the 5th step, and moving 10 steps up would bring Mason to the top (15th step). Moving 5 steps down would bring Mason to the ground (step 0).

Therefore, the appropriate domain for h would be integers within the range -5≤n≤10. This means option A is the correct choice for both the type of number and the domain.