Suppose that the price of gasoline is $3.09 per gallon. (a) generate a formula that describes the cost, , of buying gas as a function of the number of gallons of gasoline, , purchased. (b) what is the independent variable? the dependent variable? (c) does your formula represent a function? explain. (d) if it is a function, what is the domain? the range? (e) generate a small table of values and a graph.

a) C = C0 + 3.09*n

b) Dependent: cost of buying gas

   Independent: price of gasoline per gallon

c) It is a function

d) Domain = IR. Range = [0,inf]

Step-by-step explanation:

a) The most realistic formula to describe the cost C of buying gas as a function of the number n of gallons of gasoline purchased is a formula that has as initial fixed price C0 plus the cost paid for each gallon.

So C(n) = C0 + 3.09*n

b) The independent variable is the one that is changed or controlled. So in this problem, the independent variable is n, the price of the gallon. The dependent variable is the one that will change it's value when the independent value is changed. In this problem, as n is changed, it changes C too. So C is the dependent variable.

c) For this to be a function, if C(a) = C(b), then a = b. Lets see

C(a) = C(b)

C0 + 3.09a = C0 + 3.09b

3.09a = C0 + 3.09b - C0

3.09a = 3.09b

a = b

It is a function

d) There are no squares, nor fractions, nor logarithms, so there are no restrictions and the domain is the IR.

Since n cannot be negative(you can't buy negative gallons of gasoline), the smallest value of the range will be when n = 0. So the smallest value of the range is C0.

There is no limit of n, and it is an increasing function. So the upper bound of the range is infinity.

e) n = 0, C(0) = C0

   n = 1, C(1) = C0 + n

   n = 2, C(2) = C0 + 2n

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