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In a board game, a certain number of points is awarded to a player upon rolling a six sided die (labeled 1 to 6) according to the function f(x) = 6x - 6. Find and interpret the given function values and determine an appropriate domain for the function.

User Tobigue
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Final Answer:

The domain for the function is the set of all possible outcomes of rolling a six-sided die, which is D = {1, 2, 3, 4, 5, 6}.

Step-by-step explanation:

Let's interpret the function f(x) = 6x - 6, where x represents the outcome of rolling a six-sided die.

Now, we will evaluate the function at each possible outcome of the die roll and interpret the results:

1. If x = 1 (rolling a 1), then f(1) = 6(1) - 6 = 6 - 6 = 0 points.
2. If x = 2 (rolling a 2), then f(2) = 6(2) - 6 = 12 - 6 = 6 points.
3. If x = 3 (rolling a 3), then f(3) = 6(3) - 6 = 18 - 6 = 12 points.
4. If x = 4 (rolling a 4), then f(4) = 6(4) - 6 = 24 - 6 = 18 points.
5. If x = 5 (rolling a 5), then f(5) = 6(5) - 6 = 30 - 6 = 24 points.
6. If x = 6 (rolling a 6), then f(6) = 6(6) - 6 = 36 - 6 = 30 points.

Now let’s interpret these results:
- For a roll of 1, the player gets no points.
- For a roll of 2, the player gets 6 points.
- For a roll of 3, the player gets 12 points.
- For a roll of 4, the player gets 18 points.
- For a roll of 5, the player gets 24 points.
- For a roll of 6, the player gets 30 points.

Given the context of the function, the domain should be the set of all possible outcomes of rolling a six-sided die. Therefore, an appropriate domain for this function would be D = {1, 2, 3, 4, 5, 6}, which are the only possible rolls you can get with a standard die.

In conclusion, the function f(x) = 6x - 6 assigns a certain number of points to a player depending on the roll of a die and we have determined that the domain which fits the real world context of rolling a die should consist only of the integers 1 through 6. Each outcome in this domain corresponds to a specific point score calculated by the given function.

User Michel Kansou
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