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, ...}.