Curve Sketching

Follow these steps for sketching a curve.

  1. Identify the general shape of the curve and whether it is a negative or positive etc.
  2. Identify the y-intercept – put in x=0 to see where the graph cuts the y-axis.
  3. Factorise the cubic (if you can) and identify the roots of the cubic – this is where the graph should cut or touch the x-axis.
  4. Place the curve so that it cuts the x and y axes at the correct points making sure that the curve bounces off the x axis at any repeated roots.

You may also be required to perform transformations of a given curve and you should also know how to sketch the reciprocal functions. Practice sketching cubics, transformations and reciprocal functions below.