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
Plz help with this question.
To find the domain and range of the function c(x) = 10x - 50, we need to understand the context of the problem.
In this case, the function represents Andrea's profit, which is determined by the number of candles sold (x). Let's break it down:
Domain:
The domain refers to the set of values that x can take. In this case, x represents the number of candles sold. Since you can't sell a fraction of a candle or a negative number of candles, the domain should be a set of non-negative integers. Therefore, the domain is:
Domain = {0, 1, 2, 3, ...}
Range:
The range refers to the set of values that c(x) can take. In this case, c(x) represents the profit from selling x candles. To find the range, we need to consider that the profit can be positive, negative, or even zero.
If Andrea sells zero candles (x = 0), her profit would be c(0) = 10(0) - 50 = -50. So, the minimum value of c(x) is -50. However, as x increases, the profit will increase as well since selling more candles generates more profit.
Since there is no maximum number of candles Andrea can sell, the profit (c(x)) can increase indefinitely. Therefore, the range is:
Range = {y | y ≥ -50}
To summarize:
- Domain: {0, 1, 2, 3, ...}
- Range: {y | y ≥ -50}
Remember, the domain represents the valid inputs (number of candles sold), and the range represents the possible outputs (profit).
To determine the domain and range of the function c(x) = 10x - 50, we need to consider the limitations and possible values for the input (x) and output (c(x)).
Domain:
In this case, the domain represents the set of all possible values for x, which will typically be influenced by any restrictions or limitations on the independent variable. However, in this particular situation, there are no specific restrictions given regarding the number of candles Andrea can make, so the domain can be considered as all real numbers. Therefore, the domain is (-∞, ∞).
Range:
The range represents the set of all possible values for c(x), which is the profit Andrea can make from selling the candles. The function c(x) = 10x - 50 indicates that the profit can be positive or negative, depending on various factors like the number of candles (x) sold.
To find the range, we consider the lowest and highest possible values that the function can output. Given that the cost of supplies is a fixed expense of $50, the profit (c(x)) can be negative if the number of candles sold is less than 5, which would result in a loss.
So, the range of the function is (-∞, ∞), indicating that the profit can be any real number, both positive and negative.
geez - impatient much?
The domain of any polynomial is all real numbers
c(x) is a linear function, so it's a straight line that extends indefinitely both up and down. So, the range is also all real numbers.
Did you try graphing it? Always start with that.