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Broad Topics >

Coordinates and Coordinate Geometry > Families of Graphs

##### Age 16 to 18 Challenge Level:

Sketch the graphs for this implicitly defined family of functions.

##### Age 16 to 18 Challenge Level:

Sketch the members of the family of graphs given by y =
a^3/(x^2+a^2) for a=1, 2 and 3.

##### Age 16 to 18 Challenge Level:

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

##### Age 16 to 18 Challenge Level:

Investigate the family of graphs given by the equation x^3+y^3=3axy
for different values of the constant a.

##### Age 16 to 18 Challenge Level:

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.