Drawing and Sketching of Functions

Drawing and Sketching of Functions

General Concepts

  • The process of drawing and sketching functions is a key component of graphical algebra.
  • This concept involves representing mathematical functions visually using a set of axes.

Functions and Graphs

  • Linear functions have a constant rate of change and their graphs are straight lines.
  • Quadratic functions have a variable squared as their highest power. Their graphs typically form a parabola.
  • Cubic functions contain a variable raised to the power of three. Their graphs can take on a variety of shapes with turning points.
  • Exponential functions rise or decay rapidly and their graphs vary accordingly.
  • Trigonometric functions such as sine, cosine and tangent produce regular, oscillating graphs.

Key Steps in Drawing

  • Determine the type of function you are dealing with. Understanding the form of the function will guide how you sketch its graph.
  • Identify and plot any intercepts with axes. These are points where your function crosses the x or y axis.
  • For quadratic functions, find the vertex of the parabola (the turning point) and plot this.
  • Consider the end behavior of the function as x tends to positive or negative infinity to determine the general direction of the graph.
  • Sketch the curve using the plotted points as a guide. Include any important features of the function.

Important Reminders

  • Always consider the domain and range of the function. These will provide boundaries within which to sketch your graph.
  • Where necessary, use a table of values to find exact points on the graph.


  • Mastering the sketching of functions is immensely useful within further mathematics. It can help make abstract concepts more concrete, and can simplify the understanding of more complex mathematical relationships.