I have a young teacher that has not explained this very well and I am confused, any help or steps?

Question

Tara's car travels about 25 miles on one gallon of gas. She has between 10 and 12 gallons of gas in the tank. List the independent and dependent. Find the reasonable domain and range values. Write the reasonable domain and range as inequalities

Answer 1

Tara's car gets:   25 miles per 1 gallon,    written as    25 mi/gal

The units are important; this could also be written as  (1/25) gal/mi      (1 gallon per 25 miles)

 

There are between 10 and 12 gallons in the tank.  This is written as:

       10 < x < 12        (now, "between" usually does not include the endpoints, so I didn't write  10 ≤ x ≤ 12 ).

 

The distance Tara's car can travel depends on the amount of gas in the tank.  Normally, we think of "more gas means more distance."  That is, "Which one depends on the other?"  (but in this case, it is also true that "going on a longer trip means that Tara must buy more gas.")

 

So, gas is the independent variable; distance is the dependent variable.  We would express the function as:

             distance = f(amount of gas)

 

The domain specifies what values the independent variable may have.     10 < gal < 12

                              "between 10 and 12 gallons of gas in the tank"

 

The range specifies what values the dependent variable may have as a result:

        (10 gal)*(25 mi/gal) < distance < (12 gal)*(25 mi/gal)

               250 mi < distance < 300 mi           [notice how gal cancels out, leaving only mi]

Answer 2

The distance she can go depends on how much gas her car contains.

 

Let x = gallons of gas       ----->   independent

Let y = distance traveled    ---->  dependent

 

 

The domain is the set of x values in which any function exists.  Since she is between 10 and 12 gallons of gas, her domain is

 

10 < x < 12

 

 

The range is the set of y values that satisfies the function within its domain.  So we evaluate the number of miles. 

 

 

1 gallon of gas = 25 miles

 

 

Using this conversation factor to find the distance

 

10 gallons of gas = 250 miles

 

11 gallons of gas = 275 miles

 

12 gallons of gas = 300 miles

 

 

The range is     

 

250 < y < 300