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 on the first day?
Plz help with this question.
since she can only sell whole candles, the domain is {0,1,...,8}
The range is the values of c(x) for each of those x-values.
To determine the domain and range of the function, we need to understand what values we can use as inputs (x) and what values we can expect as outputs (c(x)).
In this case, Andrea is selling candles, and she plans to sell up to 8 candles on the first day. This means the input (x) can take values from 0 up to 8, as she cannot sell a negative number of candles or sell more than 8 candles on the first day.
Domain:
The domain of the function represents the set of possible values for the input (x). In this case, the domain would be the set of natural numbers from 0 to 8.
Domain: {0, 1, 2, 3, 4, 5, 6, 7, 8}
Range:
The range of the function represents the set of possible values for the output (c(x)). In this case, the function c(x) = 10x - 50 represents Andrea's profit. By substituting the values in the domain into the function, we can obtain the corresponding values of Andrea's profit.
c(0) = 10(0) - 50 = -50
c(1) = 10(1) - 50 = -40
c(2) = 10(2) - 50 = -30
c(3) = 10(3) - 50 = -20
c(4) = 10(4) - 50 = -10
c(5) = 10(5) - 50 = 0
c(6) = 10(6) - 50 = 10
c(7) = 10(7) - 50 = 20
c(8) = 10(8) - 50 = 30
From the calculations, we can see that the range of the function includes both positive and negative values, ranging from -50 to 30.
Range: {-50, -40, -30, -20, -10, 0, 10, 20, 30}
Therefore, the domain is {0, 1, 2, 3, 4, 5, 6, 7, 8}, and the range is {-50, -40, -30, -20, -10, 0, 10, 20, 30}.
To find the domain and range of the function, we need to understand what each term represents in the given function.
In this case, "c(x)" represents the profit made by selling "x" number of candles. The function is defined as c(x) = 10x - 50, where "10x" represents the revenue earned from selling "x" candles and $50 represents the cost of supplies.
The domain of the function is the set of possible input values for "x." Since Andrea is selling candles, the number of candles sold cannot be negative, and there is likely a limit on the number of candles she can sell. In this scenario, it states that Andrea sells up to 8 candles on the first day. Therefore, the domain of the function is {x: 0 ≤ x ≤ 8}.
To find the range of the function, we need to determine the possible values of c(x). Since the function c(x) = 10x - 50 represents the profit, it can take any real value. However, considering the context, it is reasonable to assume that the profit should be non-negative. Therefore, the range of the function is {c(x): c(x) ≥ 0}.
To summarize:
- Domain: {x: 0 ≤ x ≤ 8}
- Range: {c(x): c(x) ≥ 0}