Functions and Graphs - Stage 4

Parabolic Patterns

Stage: 4 and 5 Challenge Level:

The illustration shows the graphs of fifteen functions. Two of them have equations y=x^2 and y=-(x-4)^2. Find the equations of all the other graphs.

Cubics

Stage: 4 and 5 Challenge Level:

Knowing two of the equations find the equations of the 12 graphs of cubic functions making this pattern.

Steady Free Fall

Stage: 4 Challenge Level:

Can you adjust the curve so the bead drops with near constant vertical velocity?

Minus One Two Three

Stage: 4 Challenge Level:

Substitute -1, -2 or -3, into an algebraic expression and you'll get three results. Is it possible to tell in advance which of those three will be the largest ?

Tangled Trig Graphs

Stage: 5 Challenge Level:

Can you work out the equations of the trig graphs I used to make my pattern?

Back Fitter

Stage: 4 Challenge Level:

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

Exploring Quadratic Mappings

Stage: 4 Challenge Level:

Explore the relationship between quadratic functions and their graphs.

What's That Graph?

Stage: 4 Challenge Level:

Can you work out which processes are represented by the graphs?

Short Problems

Stage: 4 Challenge Level:

A collection of short Stage 4 problems on graphs of functions.