Question

The distance in miles a car travels, y, after

using x gallons of fuel can be modeled by a
linear function. A car has 20 gallons of fuel
and travels 15 miles per gallon. For one
tank of gas, what are the domain and range
for this situation?

Domain:
Range:

Answer 1

The domain represents the set of possible values for the independent variable, which in this case is the number of gallons of fuel used (x). Since the car has 20 gallons of fuel, the domain will be the interval [0, 20] because the car cannot use a negative amount of fuel and it also cannot use more than the available 20 gallons.

The range represents the set of possible values for the dependent variable, which in this case is the distance traveled (y). The car travels 15 miles per gallon of fuel. So, for one tank of gas (20 gallons), the car will travel 20 gallons * 15 miles/gallon = 300 miles. Therefore, the range will be the interval [0, 300] since the distance traveled cannot be negative and it also cannot exceed 300 miles.

To summarize:

Domain: [0, 20]

Range: [0, 300]

These intervals represent all the possible values for the number of gallons of fuel used and the distance traveled for this situation.

Explanation:

Answer 2

`\textsf{ Domain}:\sf 0 \leq x \leq 20 \textsf{ or } [0,20]`

`\textsf{Range}: \sf 0 \leq y \leq 300 \textsf{ or } [0,300]`

Explanation:

Since the distance in miles a car travels, y, after using x gallons of fuel can be modeled by a linear function.

So, we can find the domain and range.

Now, here

The domain is the set of all possible values of x, which is the number of gallons of fuel used.

Since the car has a 20-gallon tank, the domain is:

`\sf 0 \leq x \leq 20 \textsf{ or } [0,20]`

and

The range is the set of all possible values of y, which is the distance traveled.

Since the car travels 15 miles per gallon, the range is:

`\sf 0 \leq y \leq 300 \textsf{ or } [0,300]`