Let's analyze the details given in the problem first.
1. Truck Capacity: Danny's truck can hold up to 20 gallons of gas.
2. Mileage: The truck averages 17 miles per gallon.
3. Function: [tex]\( M(g) = 17g \)[/tex] where [tex]\( M(g) \)[/tex] is the number of miles traveled on [tex]\( g \)[/tex] gallons of gas.
We'll define the domain and range for the function [tex]\( M(g) \)[/tex].
### Domain:
The domain represents the possible values for [tex]\( g \)[/tex], which is the number of gallons of gas. Since the truck's fuel tank can hold up to 20 gallons:
- The minimum value of [tex]\( g \)[/tex] is 0 (an empty tank).
- The maximum value of [tex]\( g \)[/tex] is 20 (a full tank).
Thus, the domain ([tex]\( D \)[/tex]) is [tex]\( 0 \leq g \leq 20 \)[/tex].
### Range:
The range represents the possible values for [tex]\( M(g) \)[/tex], which is the number of miles traveled. Using the given function [tex]\( M(g) = 17g \)[/tex]:
- When [tex]\( g \)[/tex] is 0 gallons, [tex]\( M(0) = 17 \times 0 = 0 \)[/tex] miles.
- When [tex]\( g \)[/tex] is 20 gallons, [tex]\( M(20) = 17 \times 20 = 340 \)[/tex] miles.
Thus, the range ([tex]\( R \)[/tex]) is [tex]\( 0 \leq M(g) \leq 340 \)[/tex].
### Conclusion:
Given the above analysis, the reasonable domain and range for the function [tex]\( M(g) = 17g \)[/tex] are:
- [tex]\( D: 0 \leq g \leq 20 \)[/tex]
- [tex]\( R: 0 \leq M(g) \leq 340 \)[/tex]
So the correct answer is:
B.
- [tex]\( D: 0 \leq g \leq 20 \)[/tex]
- [tex]\( R: 0 \leq M(g) \leq 340 \)[/tex]
