Which statements represent the function of the yearly cost in dollars, y, based on x, the number of game tokens purchased for a member of the arcade? Check all that apply.
B,c,e
To determine the function of the yearly cost in dollars, we need to identify the statements that represent this relationship.
A function is essentially a rule that relates one set of values (x, the number of game tokens purchased) to another set of values (y, the yearly cost in dollars). In other words, for every value of x, there should be a corresponding value of y.
Here are some statements to consider:
1. "The yearly cost is $50 plus $5 for each game token purchased"
2. "The yearly cost is $10 for the first 2 game tokens and $3 for each additional game token"
3. "The yearly cost is $20 for the first 5 game tokens and $2 for each additional game token"
4. "The yearly cost is $30 for each game token purchased"
To determine which statements represent the function, we need to check if they consistently relate the number of game tokens purchased (x) to the yearly cost in dollars (y).
Let's analyze each statement:
1. "The yearly cost is $50 plus $5 for each game token purchased"
This statement represents a linear function, where the yearly cost increases by $5 for each additional game token purchased. It is a valid representation of the function.
2. "The yearly cost is $10 for the first 2 game tokens and $3 for each additional game token"
This statement represents a piecewise function, where the cost is different for the first 2 game tokens and then changes for each additional game token. It is a valid representation of the function.
3. "The yearly cost is $20 for the first 5 game tokens and $2 for each additional game token"
Again, this statement represents a piecewise function, where the cost is different for the first 5 game tokens and then changes for each additional game token. It is a valid representation of the function.
4. "The yearly cost is $30 for each game token purchased"
This statement represents a constant function, where the yearly cost remains the same regardless of the number of game tokens purchased. It is a valid representation of the function.
Based on the analysis, statements 1, 2, 3, and 4 all represent the function of the yearly cost in dollars based on the number of game tokens purchased.