Graph sketching

problem
MathsJam jars

Age

14 to 16

Challenge level

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?
problem
Quartics

Age

16 to 18

Challenge level

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

Age

16 to 18

Challenge level

Show without recourse to any calculating aid that 7^{1/2} + 7^{1/3} + 7^{1/4} < 7 and 4^{1/2} + 4^{1/3} + 4^{1/4} > 4 . Sketch the graph of f(x) = x^{1/2} + x^{1/3} + x^{1/4} -x
problem
Cocked hat

Age

16 to 18

Challenge level

Sketch the graphs for this implicitly defined family of functions.
problem
Pitchfork

Age

16 to 18

Challenge level

Plot the graph of x^y = y^x in the first quadrant and explain its properties.
problem
Maths filler 2

Age

14 to 16

Challenge level

Can you draw the height-time chart as this complicated vessel fills with water?
problem
Squareness

Age

16 to 18

Challenge level

The family of graphs of x^n + y^n =1 (for even n) includes the circle. Why do the graphs look more and more square as n increases?
problem
Scientific curves

Age

16 to 18

Challenge level

Can you sketch these difficult curves, which have uses in mathematical modelling?
problem
A close match

Age

16 to 18

Challenge level

Can you massage the parameters of these curves to make them match as closely as possible?
problem
Take your dog for a walk

Age

7 to 11

Challenge level

Use the interactivity to move Pat. Can you reproduce the graphs and tell their story?