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

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 x3±0
The x = 3 construction line allows the limits to be plotted as x3 from either side.

Adding this line then allows us to sketch the curve:

See also: Inflection, Jordan Curve.

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Subjects: Mathematics