 |
| Test for Functions (Summary) |
|
| (a) (i) The relation should be one-one or many-one, and |
| |
| (ii) Every first element is mapped which means that every pre-image should have an image. |
| |
| (b) For graphs: |
| |
| Draw a line parallel to the y-axis. If it cuts the graph only in one point, then the graph represents a function. If it cuts in more than one point then the relation is not a function (because the relation will become one-many and for one value of x we will have two or more values of y). |
| |
| The following graphs represent functions: |
| |
| Function; {(x, y) : y = x + 1} |
| |
 |
| |
Function; f(x) =  |
| |
 |
| |
| Function; {(x, y):y = x2} |
| |
 |
| |
| The following graphs do not represent functions: |
| |
| Not function; {(x, y) ; x2 + y2 = 9} |
| |
 |
| |
Not function;  |
| |
 |
| |
| Not function; f(x) = {(x, y): x = y2} |
| |
 |
| |
