Andrea is selling candles as a fundraiser. she spent $50 on supplies for making the candles. she plans to sell the candles for $10 each. her profit can be modeled by c(x)=10x-50. what is the domain and range of the function if she sells up to 8 candles a day?
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To determine the domain and range of the function, we first need to understand what the function represents. In this case, the function c(x) represents Andrea's profit from selling candles, where x is the number of candles she sells.
The domain of a function refers to the set of all possible inputs (in this case, the number of candles sold), and the range refers to the set of all possible outputs (the profit).
In the given function c(x) = 10x - 50, Andrea is selling up to 8 candles a day. So, in this case, the domain would be the set of all possible values for x, which ranges from 0 to 8. Therefore, the domain is {0, 1, 2, 3, 4, 5, 6, 7, 8}.
To find the range, we need to understand how the output (profit) changes with different inputs (number of candles sold). The function c(x) = 10x - 50 implies that for each additional candle sold, Andrea's profit increases by $10. Additionally, the constant term of -50 represents the initial investment (spending $50 on supplies), which reduces her profit irrespective of the number of candles she sells.
Given that the profit is dependent on the number of candles sold, we can conclude that the range is the set of all possible profits. Since the profit can vary from negative to positive values, the range of the function c(x) = 10x - 50 would be (-∞, ∞), where (-∞ represents negative infinity and ∞ represents positive infinity).
Therefore, the domain is {0, 1, 2, 3, 4, 5, 6, 7, 8}, and the range is (-∞, ∞).