The gizmo store sells gizmos. You pay $3 for the first 3 gizmos and $0.75 for each additional Gizmo.

Question

a. Define an independent and a dependent variable and describe a function that arises from this scenario. Give any restrictions on the values of the independent variable. 

b. Find an equation for the function and explain why the equation is valid. 

Answer 1

 

 The independent variable N is the number of gizmos purchased.

 The dependent variable C is the cost of purchasing N gizmos.

 

 The domain is the set of non-negative integers  greater than 2, namely N=3,4,5,....

 

 The function is C(n) = 3 + 0.75 * ( n - 3)

 

 For n = 3, the cost is C(3) = 3 + 0.75 * (3-3) = 3 + 0.75*0 = 3 + 0 = 3

 For n = 4, the cost is C(4) = 3 + 0.75 * (4-3) = 3 + 0.75*1  = 3 + 0.75 = 3.75

 For n = 5, the cost is C(5) = 3 + 0.75 * (5-3) = 3 + 0.75*2 = 3 + 1.50 = 4.50

 

 This is because you cannot buy less than 3 gizmos. You must buy 3 gizmos

 as a minimum.  Any number of gizmos purchased in excess of 3 costs 75 cents,

  So you subtract 3 from the number of gizmos purchased then multiply by 75 cents.

  Finally the original $3 is added.