Given that the car can travel 32 miles for each gallon of gasoline and that the fuel tank holds 17 gallons, we can determine the domain and range for the function \( d(x) = 32x \), which represents the distance \( d(x) \) (in miles) that the car can travel with \( x \) gallons of gasoline.
Part 1: Domain
Since the car's tank can hold a maximum of 17 gallons, the domain is limited to the interval where \( x \) is from 0 gallons (if the tank is empty) to 17 gallons (the full tank). Thus, the appropriate domain is:
\[ 0 \leq x \leq 17 \]
This means the correct choice for the domain is:
A. \( 0 \leq x \leq 17 \)
Part 2: Range
Next, we can find the range of the function \( d(x) = 32x \).
- When \( x = 0 \) (the tank is empty), \( d(0) = 32 \cdot 0 = 0 \).
- When \( x = 17 \) (the tank is full), \( d(17) = 32 \cdot 17 = 544 \).
Thus, the range of the function \( d(x) \) is from 0 miles to 544 miles:
\[ 0 \leq d(x) \leq 544 \]
Summary
- Domain: \( [0, 17] \)
- Range: \( [0, 544] \)
Graph
To graph the function, we can plot the points:
- At \( x = 0 \), \( d(0) = 0 \).
- At \( x = 17 \), \( d(17) = 544 \).
Connecting these points will give us a straight line because \( d(x) = 32x \) is a linear function.
Here's a simple representation:
Distance (miles)
|
| • (17, 544)
| /
| /
| /
| /
| /
| /
| • (0, 0)
|
|____________________
Gallons of Gas
(0 to 17)
This graph illustrates how the distance traveled increases linearly as more gasoline is used, within the defined domain of 0 to 17 gallons.