Question

the amount of gasoline, in gallons, remaining in a fuel tank is modeled by the linear function $g(m) = 23 - 0.05m$, where $m$ represents the number of miles driven. determine and interpret the domain of the function.
$0 \leq m \leq 460$, the vehicle will burn fuel from miles 0 to 460
$0 \leq m < 23$, the amount of gasoline decreases from 23 to 0 gallons.
$0 \leq m \leq 460$, the amount of gasoline decreases from 460 to 0 gallons.
$0 \leq m < 23$, the vehicle will burn fuel from miles 0 to 23

Explanation:

Step1: Find the lower bound of the domain

The number of miles driven \(m\) cannot be negative. So, \(m\geq0\).

Step2: Find the upper bound of the domain

Set \(g(m) = 0\) (since the amount of gasoline cannot be negative).

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LATEXBLOCK0
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Answer:

The domain of the function is \(0\leq m\leq460\). This means the vehicle will burn fuel from miles \(0\) to \(460\). So the correct option is \(0\leq m\leq460\), the vehicle will burn fuel from miles \(0\) to \(460\).