To determine the nature of the function that models the outcome of each roll, and to find its domain and range, we need to analyze the given information.
### Nature of the Function
A function is called discrete if it deals with distinct and separate values. A function is continuous if it deals with a continuous range of values, meaning there are no gaps in the possible outcomes.
In the context of rolling a number cube:
- Each roll of the cube has specific, countable outcomes: 1, 2, 3, 4, 5, or 6.
- The function that models the outcome of rolling a number cube pairs each roll (input) with a specific outcome (output).
Since the function deals with distinct, separate values corresponding to each roll, the function is discrete.
### Domain of the Function
The domain of the function is the set of all possible input values. Here, the input values are the numbers that represent the sides of the cube being rolled. Therefore, the domain is:
[tex]\[ \text{Domain} = \{1, 2, 3, 4, 5, 6\} \][/tex]
### Range of the Function
The range of the function is the set of all possible output values that the function can take based on the given outcomes. We extract these from the table:
- The outcomes for each roll are: 4, 3, 6, 3, 5, 4.
Listing the unique values, we get:
[tex]\[ \text{Range} = \{3, 4, 5, 6\} \][/tex]
### Summary
- Nature of the function: Discrete
- Domain: \{1, 2, 3, 4, 5, 6\}
- Range: \{3, 4, 5, 6\}
By analyzing the table and outcomes, we conclude that the function is discrete, with the domain being 1 through 6, and the range being 3, 4, 5, and 6.
