# Case Study: Function Establishes the Relationship That Exists

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Function establishes the relationship that exists between different variables, more precisely, between the input and output variables. The input variables will be linked to the output result through a general formula or function: through the input of the variables into the formula, the final output will result. One important condition for a relation to be considered a function is for each x value to result one and solely one f (x) value.

A linear function is a function which has only one variable and it is, at the same time, a first degree function. The general formula of a linear function is f (x) = ax + b, where a and b are real constants and x is the input variable.

As previously mentioned, the standard form of a linear function is f (x) = ax + b.

The slope of a line is a in the function f (x) = ax + b. As such, the formula to calculate a is a = (f (x) -- b)/a

Let C. be the number of cups that are sold and P. The price for which the cups are sold. The total money that can be raised through the lemonade stand is given by the function f (P) = C * P, following the notation previously mentioned. In that…
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