Question

question 1 - 16
a vehicle has a maximum fuel capacity of 20 gallons. the amount of fuel left in the vehicle, ( g(x) ), after traveling ( x ) miles is represented by the graph below.
which statement is true?
when the gas tank is full, the vehicle can travel 140 miles before it runs out of fuel.
when the gas tank is full, the vehicle can travel 20 miles before it runs out of fuel.
the range of the function is ( 0 leq g(x) leq 140 ).
the domain of the function is ( 0 leq x leq 20 ).

Explanation:

Step1: Analyze the graph

The \(y\) - axis represents the fuel in gallons (\(g(x)\)) and the \(x\) - axis represents the miles traveled. When the fuel tank is full (\(g(x)=20\) gallons), we need to find the value of \(x\) when \(g(x) = 0\). From the graph, when \(g(x)=0\), \(x = 140\) miles.

Step2: Analyze the range

The range of a function \(y = g(x)\) is the set of all possible \(y\) - values. The fuel \(g(x)\) starts at \(20\) gallons (when \(x = 0\)) and goes to \(0\) gallons (when \(x=140\)). So the range is \(0\leq g(x)\leq20\) (since the maximum fuel capacity is \(20\) gallons). The domain is \(0\leq x\leq140\) (because when \(g(x) = 0\), \(x = 140\) and when \(g(x)=20\), \(x = 0\)).

Answer:

When the gas tank is full, the vehicle can travel 140 miles before it runs out of fuel.