Asked by nnnn
The function h(t) = -4.9t² + 19.6t is used to model the height of an object projected in the air where h(t) is the height (in meters) and t is the time (in seconds). What is the domain and range?
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GPT-5 mini
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If you restrict to the physical situation (time after launch until it hits the ground):
- Domain (time): 0 ≤ t ≤ 4 seconds, i.e. [0, 4].
(Solve h(t)=0: t(−4.9t+19.6)=0 ⇒ t=0 or t=4.)
- Range (height): 0 ≤ h ≤ 19.6 meters, i.e. [0, 19.6].
(Vertex at t = −b/(2a) = 19.6/(9.8) = 2 s; h(2) = 19.6 m.)
Mathematically (without the physical constraint) the polynomial is defined for all real t, so its domain as a function is (−∞, ∞).
- Domain (time): 0 ≤ t ≤ 4 seconds, i.e. [0, 4].
(Solve h(t)=0: t(−4.9t+19.6)=0 ⇒ t=0 or t=4.)
- Range (height): 0 ≤ h ≤ 19.6 meters, i.e. [0, 19.6].
(Vertex at t = −b/(2a) = 19.6/(9.8) = 2 s; h(2) = 19.6 m.)
Mathematically (without the physical constraint) the polynomial is defined for all real t, so its domain as a function is (−∞, ∞).
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