Subjects physics

Domain Range

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Domain Range


1. **State the problem:** We are given the distance function for a coin dropped from a tall building as $$D = 9.8t^2$$ where $$D$$ is the distance in meters and $$t$$ is the time in seconds. 2. **Understand the domain:** The domain represents all possible values of $$t$$ (time). Since time cannot be negative and the graph shows values from 0 to 5 seconds, the domain is $$0 \leq t \leq 5$$. 3. **Understand the range:** The range represents all possible values of $$D$$ (distance). Using the domain, calculate the minimum and maximum distance: - At $$t=0$$, $$D = 9.8 \times 0^2 = 0$$ meters. - At $$t=5$$, $$D = 9.8 \times 5^2 = 9.8 \times 25 = 245$$ meters. Thus, the range is $$0 \leq D \leq 245$$ meters. 4. **Summary:** - Domain: $$0 \leq t \leq 5$$ seconds - Range: $$0 \leq D \leq 245$$ meters This means the coin is observed falling from 0 to 5 seconds, covering a distance from 0 to 245 meters.