# Curve Sketching

- When sketching a curve there are a number of general features to look for:

- Symmetry (even in
*x*or even in*y*) - Points where
*y*= 0 and where*y*changes sign, the same for*x* - Look at behaviour as
*x*→ ±∞ - Look at behaviour near special points, eg assymtotes

- Symmetry (even in

**Example**- sketch the following example:
*y*changes sign at*x*= 0,*x*= 2,*x*= 3

- also, y>0 when x>0

*y*= 0 at*x*= 0 and*x*= 2,*y*~ 2/3*x*for small x

- Near
*x*= 3,*y*→ ±∞ as*x*→3±0 - The
*x*= 3 construction line allows the limits to be plotted as*x*→3 from either side.

- Adding this line then allows us to sketch the curve:

**See also: **Inflection, Jordan Curve.

**Subjects: ** Mathematics