How do I set up a functional equation?

What you need:

• paper
• Pen
• (Eraser)
• calculator

Establish the functional equation of a straight line

• The task is to find the functional equation of the corresponding points from two given points P1 and P2 Straight lines to set up.
• The general form of the function equation we are looking for is f (x) = mx + b. Here, f (x) corresponds to the y-value of the straight line, m is the slope and b is the y-axis section.
• The two unknowns m and b must be determined from the two points P1 and P2 (then you know the straight line).
• Aside from plugging into the two-point formula (which must be remembered), it is also possible to use two Equations to set up with 2 unknowns (m, b) and then to solve them.
• You know from points P1 and P2 that you have to fulfill the function equation (otherwise they will not lie on the straight line), i.e. x and y values ​​are simply inserted in f (x). An equation is obtained for P1 and for P2, in which only m and b appear as unknowns.
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Completely rational functions - this must be taken into account when calculating

Rational functions are the subject of school mathematics, mostly in the 11th grade. School year. The …

• The two equations can be used with the known methods (insert, equate, addition method) or with the calculator to solve.

Establish a functional equation for a parabola

• The task here is to find the functional equation of a quadratic function (parabola) from three (!) Given points P1, P2 and P3.
• The general form of this function we are looking for is f (x) = ax² + bx + c. Unknown here are a, b, and c, which have to be determined from the three points.
• Here, too, the coordinates of the points satisfy the functional equation. If you insert the x and y values ​​of the points one after the other into the function equation you are looking for, you get 3 equations with the 3 unknowns a, b and c.
• This system of equations can also be solved relatively easily with the known methods and with the pocket calculator.

Establish a functional equation for a completely rational function

• The game can be continued with any complexity.
• The general procedure for this case, in which the completely rational function is to be determined from certain conditions, is explained by the latter items.