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?
#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.
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, ...}.
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.
To determine whether the graph represents a discrete or continuous situation, we need to understand the difference between the two.
In a discrete situation, the values or quantities involved are distinct and separate. They are often counted or measured in whole numbers or fixed intervals. Discrete situations are represented by discrete graphs, where the points on the graph are disconnected.
On the other hand, in a continuous situation, the values or quantities involved form a continuum without any gaps or jumps. They can take on any value within a given range. Continuous situations are represented by continuous graphs, where the points on the graph are connected.
Looking at the function f(x) = 30x + 20, we can see that 'x' represents the number of pairs of weight plates added to the barbell. It can take on any non-negative integer value since you can only add whole pairs of weight plates. This indicates that 'x' is discrete, meaning the situation is discrete. Therefore, the graph represents a discrete situation.
Now let's determine the domain and range of the function. The domain of the function refers to all possible input values, while the range refers to all possible output values.
In this case, the input variable 'x' represents the number of pairs of weight plates added to the barbell. Since you can add any non-negative integer number of pairs, the domain of the function is {0, 1, 2, 3, ...} or simply the set of non-negative integers.
The output of the function is the total weight of the barbell and plates. Given that each pair of plates weighs 30 lb and there is a 20 lb barbell, the range of the function is {20, 50, 80, 110, ...} or simply the set of numbers that are 30 times a non-negative integer plus 20.
To summarize:
- The graph represents a discrete situation.
- The domain of the function is {0, 1, 2, 3, ...}.
- The range of the function is {20, 50, 80, 110, ...}.