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.