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 sense, the idea would be to maximize f (P). From this equation, C = f (P)/P
6. Starting with the general format of a function, f (x) = ax + b, we can build a system of equation to identify a and b, as such:
-3 a+ b = 0 and a + b = 12. From this system of equation, subtracting the first equation from the second, -4a = -12 and a = 3. As a result, b = 9. The resulting function is f (x) = 3x+9.
This can be verified with one of the other value from the table, for example x=3. Putting x=3 in the function, the resulting f (3) = 18, which is verified by the actual value of f (x) in the table
7. a. This is a function where the speed that you drive with is the variable and the connecting element is the distance to work.
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