Subjects algebra

Domain Range D8B533

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1. **State the problem:** We have a car traveling a distance $d$ as a function of time $t$. The car travels 425 miles at a speed of 50 miles per hour. We need to find the domain and range of the function $d(t)$. 2. **Understand the function:** The distance traveled is given by the formula $$d = ext{speed} \times t$$ where speed is 50 miles per hour. 3. **Calculate the time taken:** To travel 425 miles at 50 mph, time $t$ is $$t = \frac{d}{\text{speed}} = \frac{425}{50} = 8.5 \text{ hours}$$ 4. **Determine the domain:** Time $t$ starts at 0 (when the car starts) and goes up to 8.5 hours (when the car finishes traveling 425 miles). So, the domain is all real values from 0 to 8.5. 5. **Determine the range:** Distance $d$ starts at 0 miles and increases to 425 miles as time goes from 0 to 8.5 hours. So, the range is all real values from 0 to 425. 6. **Conclusion:** The domain is $[0, 8.5]$ and the range is $[0, 425]$. **Answer:** The domain is all real values from 0 to 8.5 and the range is all real values from 0 to 425.