A donut shop charges $0.80 per glazed donut and $2.50 per coffee. If x donuts are purchased, the total cost y of donuts and a coffee can be represented by f(x)=0.80x+2.50.
What are the domain and range of this function?
The domain of the function f(x) is the set of possible inputs or values of x. In this case, the number of donuts purchased, x, can be any non-negative whole number or zero since it doesn't make sense to purchase a negative number of donuts. Therefore, the domain is the set of non-negative whole numbers or zero, which can be represented as {0, 1, 2, 3, ...}.
The range of the function f(x) is the set of possible outputs or values of y. In this case, the total cost y can be any non-negative real number since both the cost of a donut and the cost of a coffee are non-negative. Therefore, the range is the set of non-negative real numbers, which can be represented as [0, ∞).
what is the answer
The domain of the function f(x) is {0, 1, 2, 3, ...} and the range is [0, ∞).
how would you put [0, ∞) with a iniquality
Inequality notation for [0, ∞) would be y ≥ 0. This represents all values of y that are greater than or equal to zero.
To determine the domain and range of the function f(x) = 0.80x + 2.50, we need to understand what values the variable x can take and what values the function y can output.
The domain refers to the set of possible input values for the function. In this case, x represents the number of donuts purchased. The domain is typically all the real numbers or a subset of the real numbers that makes sense in the given context. For this function, the domain can be any positive integer or zero, as it wouldn't make sense to purchase a negative number of donuts. Therefore, the domain is D: {0, 1, 2, 3, ...} (the set of non-negative integers).
The range, on the other hand, represents the set of all possible output values of the function. In this case, y represents the total cost of donuts and a coffee. Since the cost can never be negative, the range will be all the values greater than or equal to 2.50. Therefore, the range is R: {y | y ≥ 2.50}.
In summary:
Domain (x-values): D = {0, 1, 2, 3, ...} (non-negative integers)
Range (y-values): R = {y | y ≥ 2.50} (cost greater than or equal to 2.50)