Question

The function h(t) = -4.92f^2 + 17.69f + 575 is used to model the height of an object being tossed from a tall building, where h(t) is the height in meters and t is the time in seconds. What are the domain and range?

Answer 1

rounded to 3 decimal places ...

• domain: [0, 12.757]
• range: [0, 590.901]

Explanation:

The function can be put into vertex form:

h(t) = -4.92(t -(1769/984))^2 +575 +4.92(1769/984)^2

h(t) ≈ -4.92(t -1.79776)^2 +590.90122

The value of h(t) is zero for ...

t = √(590.90122/4.92) +1.79776 ≈ 12.75686

For practical purposes, the domain of the function is those values of t between the time the object is tossed and the time it hits the ground. That is, the domain is ...

0 ≤ t ≤ 12.75686

The range is the set of useful vertical heights, so extends from 0 to the maximum height, given by the vertex.

The range is 0 ≤ h(t) ≤ 590.90122.

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Alternate interpretation of the question

The function h(t) is defined for all values of t, so that could be considered the domain.

The function h(t) only gives values less than its vertex value, so the range could be considered to extend from negative infinity to that maximum.