For the relation below determine whether y is a function of

For the relation below, determine whether y is a function of x and justify your answer. y = x(18 - 2x)(13 - 2x) (this equation models the familiar open-top box, where y is the volume of the open-top box cut from a 13\" times 18\" sheet of paper when the square cutout has side length x) Is y a function of x ? The reason for my answer is... For at least one value of side length for the cutouts, two different resulting box volumes are possible The volume changes whenever the square cutout side length changes It\'s possible to achieve the same volume with two different values of x For each value of side length for the cutouts, there\'s only one resulting box volume You can\'t have a negative value of x since it represents length If you answered yes in part (a), what is the domain of this function as an equation of y and x only, disregarding the open-top box context? If y is not a function of x write DNE. If you entered yes in part (a), what is the contextual domain of this function (i.e. considering the meanings of the quantities x and y relative to the open-top box)? If y is not a function of x write DNE.

Solution

a) yes

for each value of side length for the cutouts,there\'s only one resulting box volume

b)(-,)

c)x cannot be grater than 13/2, for x =0,x =13/2, volume of box =0

domain of the function is (0, 13/2), or (0,6.5)