Question

The function below models the amount of gas, g(x)
, in gallons, left in Julia’s car after driving x
miles.

g(x)=15−0.3x

Which of the following statements correctly interprets a key feature of the function? (Select all that apply.)

(2 points)
Responses

The car starts with 0.3 gallons of gas.
The car starts with 0.3 gallons of gas.

The car starts with 15 gallons of gas.
The car starts with 15 gallons of gas.

The car gains 0.3 gallons of gas for each mile driven.
The car gains 0.3 gallons of gas for each mile driven.

The car uses 15 gallons of gas per mile.
The car uses 15 gallons of gas per mile.

The car uses 0.3 gallons of gas for each mile driven.
The car uses 0.3 gallons of gas for each mile driven.
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Answer 1

To interpret the function \( g(x) = 15 - 0.3x \), let's analyze its key features:

1. **Initial Amount of Gas**: When \( x = 0 \) (meaning the car has not yet driven any miles), the amount of gas \( g(0) \) is:
\[
g(0) = 15 - 0.3(0) = 15 \text{ gallons}
\]
This means the car starts with 15 gallons of gas.

2. **Gas Consumption per Mile**: The term \(-0.3x\) indicates that for each mile driven (each increase in \( x \)), the amount of gas decreases by 0.3 gallons. Thus, the car uses 0.3 gallons for each mile driven.

Based on this analysis, the correct statements are:

- **The car starts with 15 gallons of gas.**
- **The car uses 0.3 gallons of gas for each mile driven.**

The other statements are incorrect interpretations of the function.