Curve Sketching - Basic Techniques

Basic Techniques

The following are usually easy to carry out and give important clues as to the shape of a curve:

  • Determine the x and y intercepts of the curve. The x intercepts are found by setting y equal to 0 in the equation of the curve and solving for x. Similarly, the y intercepts are found by setting x equal to 0 in the equation of the curve and solving for y
  • Determine the symmetry of the curve. If the exponent of x is always even in the equation of the curve then the y-axis is an axis of symmetry for the curve. Similarly, if the exponent of y is always even in the equation of the curve then the x-axis is an axis of symmetry for the curve. If the sum of the degrees of x and y in each term is always even or always odd, then the curve is symmetric about the origin and the origin is called a center of the curve.
  • Determine any bounds on the values of x and y.
  • If the curve passes through the origin then determine the tangent lines there. For algebraic curves, this can be done by removing all but the terms of lowest order from the equation and solving.
  • Similarly, removing all but the terms of highest order from the equation and solving gives the points where the curve meets the line at infinity.
  • Determine the asymptotes of the curve. Also determine from which side the curve approaches the asymptotes and where the asymptotes intersect the curve.

Read more about this topic:  Curve Sketching

Famous quotes containing the words basic and/or techniques:

    “The man who is admired for the ingenuity of his larceny is almost always rediscovering some earlier form of fraud. The basic forms are all known, have all been practicised. The manners of capitalism improve. The morals may not.”
    —John Kenneth Galbraith (b. 1908)

    “It is easy to lose confidence in our natural ability to raise children. The true techniques for raising children are simple: Be with them, play with them, talk to them. You are not squandering their time no matter what the latest child development books say about “purposeful play” and “cognitive learning skills.””
    —Neil Kurshan (20th century)