The independent variable in the function P(x) = 0.01x - 29/x is the number of soft drinks sold. Thus, option (A) "The number of soft drinks sold" is correct.
The independent variable in a function is the variable that represents the input or the domain of the function, affecting the output. In the provided function P(x) = 0.01x - 29/x, the independent variable is x because it represents the number of soft drinks sold.
Option (A) "The number of soft drinks sold" correctly identifies the independent variable in this context. The function P(x) expresses the profit as a function of the quantity of soft drinks sold (x). As the quantity of soft drinks sold changes, it directly influences the profit, making it the independent variable in this function.
Option (B) "The profit in thousands of colones per week" is the dependent variable in this context. The profit depends on the number of soft drinks sold, so it is the output or dependent variable.
Options (C) and (D) are not the independent variable. Option (C) "The soft drink factory" is not a variable in the function but refers to the entity itself. Option (D) "The formula for P(x)" is not a variable but a representation of the function.
In summary, the independent variable in the function P(x) = 0.01x - 29/x is the number of soft drinks sold, making option (A) "The number of soft drinks sold" the correct answer.
The question probable may be:
The owner of a soft drink factory knows that his profit (in thousands of colones per week), as a function of the number x of soft drinks sold, is given by the equation P(x) = 0.01x - 29/x. If it is known that P ( x) is a function, what is its independent variable? (A) The number of soft drinks sold (B) The profit in thousands of colones per week (C) The soft drink factory (D) The formula for P (x) 9.