Schaubilder zuordnen über Globalverhalten und Symmetrie (für ganzrationale Funktionen)

How to Math video overview at https://howtomathe.de A brief explanation of how to recognize global progression and symmetry in function terms and graphs, and how to use this to assign and justify them, using two examples. Note 1: There is another point symmetry that is easily recognized: point symmetry with respect to a point on the y-axis. In this case, all exponents are odd, and a number without an x ​​is added at the end, e.g., in the second example for h: h(x) = 2x³ - x + 1. Here, point symmetry with respect to (0 | 1) is present, as can also be seen in the graph. Note 2: In general, the intersection point with the y-axis is also easy to read: All parts with x are then 0, and the number at the end is the y-value, e.g., f(x) = 5x² + 2x - 1 intersects at (0 | -1). This can also be used for justification (but not here, because they all have the same y-axis intercept each time, so global progression and symmetry must be used).