Question

given the linear function f(x)=3x + 50, which of the scenarios does it best represent? a bakery sells cupcakes for $50 each and offers a $3 discount for bulk orders. a factory produces 50 units of a product daily and adds 3 more when machines are working ok. a store charges $3 for each apple and has a $50 for each orange. a gym charges $50 per month and an additional $3 for each class attended.

Explanation:

Step1: Analyze the linear - function form

The linear function is \(f(x)=3x + 50\), which is in the form \(y=mx + b\), where \(m\) is the slope (rate of change) and \(b\) is the y - intercept (initial value).

Step2: Analyze each scenario

• Bakery scenario: It offers a discount, which is a subtraction - related concept and not in the form of \(y = mx + b\) as described in the given function.
• Factory scenario: Produces 50 units daily and adds 3 more when machines are working OK. If we let \(x\) be some factor related to machine - working conditions (e.g., number of days with all machines working OK), the total production \(y\) is \(y = 3x+50\). Here, 50 is the base production and 3 is the rate of additional production per unit of \(x\).
• Store scenario: Charges \(3\) for each apple and has a \(50\) related to oranges. The cost function for apples and oranges combined is not in the form \(y = 3x + 50\) in a straightforward way as the variables are for different fruits.
• Gym scenario: Charges \(50\) per month and an additional \(3\) for each class attended. If we let \(x\) be the number of classes attended, the total cost \(y\) is \(y=3x + 50\), where 50 is the base monthly cost and 3 is the cost per class.

Answer:

The factory and gym scenarios best represent the linear function \(f(x)=3x + 50\).