Since your goal is to estimate the fuel cost (in dollars) and you know that fuel costs $2.80 per gallon, the cost of v gallons of fuel is 2.80v2.80v. (The expression 2.80v2.80v represents a value that is 2.80 times as large as v). See the function machine f below. A value of d is input to the function f and the rule of f determines the corresponding value for v. The function machine gg takes a value of v as an input to the function gg and the rule of g determines the corresponding value for c`.

Our goal is to use function notation to represent the total fuel cost, in terms of the distance (in miles) of the trip. In doing so we first need to define a function, f, to determine the volume, v, of gasoline used in terms of the distance, d, of a trip.

       1. Represent v using function notation. v=_____

       2. Define a function f that determines the volume of gasoline used in terms of the distance, d, (in miles) of a trip.

       3. Define a function g that determines the fuel cost, c=g(v)c=g(v), in terms of the volume of gasoline used on the trip.

       4. Define a function g that determines the fuel cost, c, in terms of d, by substituting f(d)f(d) for v in your previous definition.

       5.Represent the total fuel cost of a 263 mile trip using function notation.

       6. Represent the difference in total cost of a 340 mile trip as compared to a 540 mile trip.

 

b) Using these two function processes we can determine and represent the cost of fuel for a road trip, c=g(f(d))c=g(f(d)), in terms of the distance, d, of the trip (in miles) by linking the functions f and g.

Evaluate g(f(d))g(f(d)) when d=1664d=1664 miles by answering the following:

      1.  Evaluate f(1664)f(1664) and explain what your answer represents.

f(1664)=f(1664)=________

           Select all that apply

1. the number of gallons of gasoline needed to drive 1664 miles

2. the number of miles one can drive on 32 gallons of gasoline

3. the cost of driving 1664 miles

      2.Use your answer from part one to evaluate g(f(1664)); then explain what your answer represents. ______

       Select all that apply:

• the cost of driving 1664 miles
• the gas mileage when driving 1664 miles
• the number of gallons of gasoline needed to drive 1664 miles

      3. We conclude that the fuel cost for driving ____  miles on a road trip is $____. By chaining two function processes together we are now able to determine the cost of fuel when driving a car that gets _____  miles per gallon on a road trip, with gas at a price of $______ per gallon.

Answer rating: 100% (QA)

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