1. **State the problem:** Karl's truck starts with 400 liters of fuel and consumes 0.8 liters per kilometer driven. We want to find the relationship between the fuel remaining and the distance driven. 2. **Formula and explanation:** The fuel remaining after driving $d$ kilometers is given by the initial fuel minus the fuel consumed: $$\text{Fuel remaining} = \text{Initial fuel} - (\text{fuel consumption per km} \times d)$$ 3. **Apply values:** Initial fuel = 400 liters Fuel consumption per km = 0.8 liters/km So, $$f(d) = 400 - 0.8d$$ 4. **Interpretation:** - When $d=0$, fuel remaining is $400$ liters. - For every kilometer driven, fuel decreases by 0.8 liters. - The function is linear with slope $-0.8$ and y-intercept $400$. 5. **Domain and range:** - Domain: $0 \leq d \leq 500$ (since $400/0.8=500$ km is max distance before fuel runs out) - Range: $0 \leq f(d) \leq 400$ 6. **Final answer:** The relationship is: $$f(d) = 400 - 0.8d$$ where $f(d)$ is the fuel remaining in liters and $d$ is the distance driven in kilometers.