constant rate HeLP

Question

assume a car uses gasoline at a constant rate. The car gas tank holds 14 gallons of gasoline. On a full tank of gas the diver drive for 86.8 miles and uses 3.1 gallons of gas. Use a function to determine how far ( in miles) the car can drive given x gallons of gas. Identify the domain and range of this function in context with the situation

HELP

Answer 1

Hey there,

For this question, we already have many of the portions defined. We know that x will equal the gallons of gas and that the person may drive 28 miles per gallon of fuel (this is from the 86.8 miles divided by the 3.1 gallons). We need to figure out miles per gallon because we have gallons and need to convert it to miles. This 28mpg conversion factor is the only way to do so.

So now, we know that we have X gallons of gas and can go 28 miles on each gallon. So, for 1 gallon we go 28, 2 goes 56, etc. We could easily build an input-output table from that. However, we can go one better. Clearly, Gallons times Miles Per Gallon is equal to Miles and we're currently solving for Y miles. So, Ymiles = Xgallons*28mpg will give us a linear function to define this formula.

The last step is to define domain and range. The fewest gallons the car could possibly have is 0, and the most is 14, so those will be maxes and mins for X and will define maxes and mins for Y. From there, domain and range are quick to find!