Students will graph various linear, quadratic, and trigonometric functions onto a coordinate plane. The completed graphs will form a picture of an octopus. Students may get creative and add color and personality to their finished octopus if desired. This activity includes the 19 functions to graph, the coordinate plane with a few initial details of the octopus drawn, and a solution key. A calculator may be necessary to help with the graphs containing points with non-integral coordinates. However, the majority of the trigonometric functions can be graphed without the assistance of a calculator. This activity reinforces the types of transformations that take place when equations change from y=sinx to y=2sinx and from y=cosx to y=cos(2x), etc.
As an extension to this activity, students could draw their own pictures and write the equations of the functions that create the picture.