Graph sketching

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

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

Bio Graphs

Age

14 to 16

Challenge level

What biological growth processes can you fit to these graphs?
problem

Guessing the Graph

Age

14 to 16

Challenge level

Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
problem

Curve Hunter

Age

14 to 18

Challenge level

This problem challenges you to sketch curves with different properties.
problem

Integration Matcher

Age

16 to 18

Challenge level

Can you match the charts of these functions to the charts of their integrals?