#8: The graph represents a continuous situation because the weights can be continuously added to the barbell in pairs.
#9:
Domain: The domain of this function represents the number of pairs of plates that can be added to the barbell. Since the number of pairs of plates cannot be negative, the domain is all non-negative integers. Therefore, the domain is x = {0, 1, 2, 3, ...} or the set of natural numbers.
Range: The range of this function represents the total weight of the barbell and plates. Since the weight is always a positive value, the range is all positive real numbers. Therefore, the range is f(x) > 0.
set of weights includes a20lb barbell and6pairs of weight plates. Each pair of plates weighs 30 lb. Ifxpairs 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?
5 answers
f(x) > 0 is not a answer
Apologies for the mistake. Let's determine the correct domain and range.
Domain: The domain represents the possible values for the independent variable, which in this case is the number of pairs of plates, x. Since we cannot have a negative number of pairs of plates, the domain is the set of non-negative integers. Therefore, the domain is x = {0, 1, 2, 3, ...} or the set of natural numbers.
Range: The range represents the set of all possible output values of the function. In this case, the output values are the total weight of the barbell and plates. Since the minimum weight is the weight of the barbell (20 lbs) and the weight can be increased by adding pairs of plates (30 lbs per pair), the range consists of all positive integer multiples of 30 plus the weight of the barbell (20 lbs). In formulaic terms, the range is given by R = {20 + 30x : x is a non-negative integer}. Therefore, the range is R = {20, 50, 80, 110, ...}.
Domain: The domain represents the possible values for the independent variable, which in this case is the number of pairs of plates, x. Since we cannot have a negative number of pairs of plates, the domain is the set of non-negative integers. Therefore, the domain is x = {0, 1, 2, 3, ...} or the set of natural numbers.
Range: The range represents the set of all possible output values of the function. In this case, the output values are the total weight of the barbell and plates. Since the minimum weight is the weight of the barbell (20 lbs) and the weight can be increased by adding pairs of plates (30 lbs per pair), the range consists of all positive integer multiples of 30 plus the weight of the barbell (20 lbs). In formulaic terms, the range is given by R = {20 + 30x : x is a non-negative integer}. Therefore, the range is R = {20, 50, 80, 110, ...}.
Given f(x)=−6(1−x), what is the value of f(−8)? (Type your answer below 👇👇) x f(x)
To find the value of f(-8), we substitute -8 into the function f(x) = -6(1 - x):
f(-8) = -6(1 - (-8))
= -6(1 + 8)
= -6(9)
= -54
Therefore, the value of f(-8) is -54.
f(-8) = -6(1 - (-8))
= -6(1 + 8)
= -6(9)
= -54
Therefore, the value of f(-8) is -54.