A set of weights includes a`20`lb barbell and`6`pairs of weight plates. Each pair of plates weighs `30` lb. If x pairs of plates are added to the barbell, the total weight of the barbell and plates in pounds can be represented by `f(x)=30x+20.`
#8: Does this graph represent a discrete or continuous situation?
#9: What is the domain & range of the function for this situation?
8: This graph represents a discrete situation because the weight plates can only be added in whole pairs, not in fractions or decimals.
9: The domain of the function is x, representing the number of pairs of weight plates added to the barbell. Since the number of pairs of weight plates cannot be negative and must be a whole number, the domain is {0, 1, 2, 3, ...} or the set of non-negative integers.
The range of the function is the total weight of the barbell and plates. Since the weight of the barbell is 20 lbs and each pair of plates weighs 30 lbs, the range is {20, 50, 80, 110, ...} or the set of numbers that are 20 lbs more than a multiple of 30.