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

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 ~ 2/3x 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.