If your car gets 32 miles per gallon of gas you need to travel 278 miles on day 1, 649 miles on day 2, and 482 miles on day 3.

What is the function? What are the domain and the range?

To solve this problem, we can use the concept of a linear function. A linear function is a mathematical model that represents a linear relationship between two variables. In this case, the two variables are the number of miles traveled (x) and the amount of gas needed (y).

Let's start by finding the equation for the linear function. Given that the car gets 32 miles per gallon of gas, we can use this information to find the number of gallons of gas needed for each day's travel.

On day 1, the car needs to travel 278 miles. To find the amount of gas needed, we divide the distance by the car's fuel efficiency:

Gallons on day 1 = 278 miles / 32 miles per gallon = 8.6875 gallons (rounded to 4 decimal places)

On day 2, the car needs to travel 649 miles. We use the same formula to find the amount of gas needed:

Gallons on day 2 = 649 miles / 32 miles per gallon = 20.28125 gallons (rounded to 5 decimal places)

On day 3, the car needs to travel 482 miles. Again, we use the formula to find the amount of gas needed:

Gallons on day 3 = 482 miles / 32 miles per gallon = 15.0625 gallons (rounded to 4 decimal places)

Now that we have the number of gallons of gas needed for each day, we can express this relationship as a linear function.

Using the point-slope form of a linear equation (y = mx + b), where m is the slope and b is the y-intercept, we have:

y = (32 gallons per mile) * x + 0

Simplifying this equation, we get:

y = 32x

The function represents the number of gallons of gas needed (y) as a function of the number of miles traveled (x). The domain of the function is all real numbers because there is no restriction on the number of miles that can be traveled. The range of the function is all real numbers greater than or equal to 0 because the number of gallons of gas needed cannot be negative.

In summary, the linear function representing the relationship between miles traveled and gallons of gas needed is y = 32x, with a domain of all real numbers and a range of all real numbers greater than or equal to 0.