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Quartics

Investigate the graphs of y = [1 + (x - t)^2][1 + (x + t^)2] as the parameter t varies.

Sine Problem

In this 'mesh' of sine graphs, one of the graphs is the graph of the sine function. Find the equations of the other graphs to reproduce the pattern.

Cocked Hat

Sketch the graphs for this implicitly defined family of functions.

Folium of Descartes

Stage: 5 Challenge Level:

Invistigate symmetry by exchanging $x$ and $y$ in the equation of the graph.

The question itself gives you guidance as to the methods to use.

Differentiation of parametric and implicit functions. Symmetry. Turning points. physics. Parameters. Functions and their inverses. Calculus generally. Graph sketching. Asymptotes. Families of Graphs.