Transformation of functions

There are 13 NRICH Mathematical resources connected to Transformation of functions

problem

Favourite

Parabolas again

Age

14 to 18

Challenge level

Here is a pattern composed of the graphs of 14 parabolas. Can you find their equations?

problem

Favourite

Exploring cubic functions

Age

14 to 18

Challenge level

Quadratic graphs are very familiar, but what patterns can you explore with cubics?

problem

Favourite

Loch ness

Age

16 to 18

Challenge level

Draw graphs of the sine and modulus functions and explain the humps.

problem

Favourite

Tangled trig graphs

Age

16 to 18

Challenge level

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

problem

Favourite

Parabolic patterns

Age

14 to 18

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.

problem

More parabolic patterns

Age

14 to 18

Challenge level

The illustration shows the graphs of twelve functions. Three of them have equations y=x^2, x=y^2 and x=-y^2+2. Find the equations of all the other graphs.