Question

A student records the height of the water in a pool each day for seven days. The function h(t) = |t-3|+14

models the height of the water h (in feet) in the pool after t days. Find the domain and range for this function and
interpret their meaning in the context of the problem.

Answer 1

When we have a function like h(t)

The domain is the set of the possible values of t.

In this case, we know that the measure lasts for 7 consecutive days, so t represents the number of days.

Then the possible values of t are:

t ∈ {1, 2, 3, 4, 5, 6, 7}

Now, let's look at the range.

The range is the set of the possible values that h(t) can take.

Then:

h(1) = I1 - 3I + 14 = 16

h(2) = I2 - 3I +14 = 15

h(3) = I3 - 3I + 14 = 14

h(4) = I4 - 3I + 14 = 15

h(5) = I5 - 3I + 14 = 16

h(6) = I6 - 3I + 14 = 17

h(7) = I7 - 3I + 14 = 18.

Then the possible values of the range are:

R = {14, 15, 16, 17, 18}

This is when we only let t to be natural numbers, if we allow t to be a real number, we will have all the values in between the natural numbers written above, then the domain is:

D: 1 ≤ t ≤ 7

And the range is:

R: 14ft ≤ h(t) ≤ 18ft