FUNCTIONS MATHEMATICS
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FUNCTIONS MATHEMATICS - Leaderboard
FUNCTIONS MATHEMATICS - Details
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| 🇬🇧 | 🇬🇧 |
| DOMAIN | PORTION OF X AXIS COVERED BY THE GRAPH |
| RANGE | PORTION OF Y AXIS COVERED BY THE GRAPH |
| ROOT | ROOT OF F(X) ID THE ABSCISSA OF THE POINT WHERE GRAPH OF F(X) CUTS THE X AXIS |
| ASYMTOTE | LINE WHICH APPEARS TO BE TANGENT AT INFINITY |
| INCREASING FUNC. | Y INCREASES WITH INC OF X |
| DECREASING FUNC. | Y DECREAASES WITH INCREASE OF X |
| MAXIMA AND MINIMA | MAXIMA AND MINIMA OF A FUNC ARE THE LARGEST AND SMALLEST VALUES OF A FUNCTION. EITHER within a given range - LOCAL MAXIMA/MINIMA OR in the entire domain - GLOBAL MAXIMA/ MINIMA |
| BOUNDED FUNCTION | IF we can draw two horizontal lines, alpha and beta such that the graph always lies between these two lines, then graph is called BOUNDED |
| UNBOUNDED GRAPHS | Graphs which are not bounded |
| SEMI Bounded graph types | Only upper bounded only lower bounded |
| EVEN FUNCTION | F(x)= f(-x) for all x belonging to domain graphs of even functions are SYMMETRICAL about y axis |
| ODD FUNCTION | F(x)= -f(x) for all x belonging to domain graphs of odd functions are SYMMETRICAL about origin, that is, opposite quadrants |
| PERIODIC FUNCTION | ALL THE FEATURES are repeated after certain intervals |
| If x --> (x-a) then shift the graph // to .. axis by |a| units 1) towards right if a is... 2) towards left if a is ... | Y positive negative |
| If y --> (y-a) then shift the graph // to .. axis by |a| units 1) if a is positive, then ... 2) if a is negative, then ... | X axis upward downward |
| X ---> (-x) | TAKE MIRROR IMAGE OF WHOLE GRAPH WRT Y AXIS |
| If x ---> ax (a>0) | DIVIE ALL THE VALUES ON X AXIA BY a |
| DIVIDE ALL THE VALUES ON y AXIS BY a if | Y---> ay (y>0) |
| X ---> |x| then, | *REMOVE THE PORTION OF GRAPH WHICH LIES ON THE LHS OF Y AXIS *TAKE REMAINING GRAPH AND ITS IMAGE WRT Y AXIS |
| Y= f(x) when f(x) ---> |f(x)| | I.e. y = |y| THE PORTION OF GRAPH BELOW X AXIS GOES ABOVE X AXIS |
| MULTIPLE TRANSFORMATIONS | * APPLY OUT TO IN * FIRST transformations on X and then on Y *if |f(x)| is present, |f(x)| |