## 1.2. Relations and Functions

### Examples 1.2.7(a):

If the graph of a function is known, how can you decide whether a function is
one-to-one (injective) or onto (surjective) ?

### Injection

If a horizontal line intersects the graph of a function in more than one place, then there are two different points*a*and

*b*for which

*f(a) = f(b)*, but

*a # b*. Then the function is not one-to-one.

**Not a one-to-one function**

### Surjection

If you place a light on the left and on the right hand side of the coordinate system, then the shadow of the graph on the*y*axis is the image of the domain of the function. If that shadow covers the range of the function, then the function is onto.

**Not an onto function**(if range is R)

**every**function can be modified to be onto by setting its range to be the image of its domain.