Transformation of functions

  • Parabolas Again
    problem
    Favourite

    Parabolas Again

    Age
    14 to 18
    Challenge level
    1 out of 3
    Here is a pattern composed of the graphs of 14 parabolas. Can you find their equations?
  • Parabolic Patterns
    problem
    Favourite

    Parabolic Patterns

    Age
    14 to 18
    Challenge level
    1 out of 3

    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.

  • Exploring cubic functions
    problem
    Favourite

    Exploring Cubic Functions

    Age
    14 to 18
    Challenge level
    2 out of 3

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

  • Tangled Trig Graphs
    problem
    Favourite

    Tangled Trig Graphs

    Age
    16 to 18
    Challenge level
    1 out of 3

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

  • Loch Ness
    problem
    Favourite

    Loch Ness

    Age
    16 to 18
    Challenge level
    2 out of 3

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

  • Sine Problem
    problem

    Sine Problem

    Age
    16 to 18
    Challenge level
    1 out of 3
    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.
  • More Parabolic Patterns
    problem

    More Parabolic Patterns

    Age
    14 to 18
    Challenge level
    1 out of 3
    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.
  • Cubic Spin
    problem

    Cubic Spin

    Age
    16 to 18
    Challenge level
    2 out of 3
    Prove that the graph of f(x) = x^3 - 6x^2 +9x +1 has rotational symmetry. Do graphs of all cubics have rotational symmetry?
  • Ellipses
    problem

    Ellipses

    Age
    14 to 18
    Challenge level
    1 out of 3

    Here is a pattern for you to experiment with using graph drawing software. Find the equations of the graphs in the pattern.

  • Painting by functions
    problem

    Painting by Functions

    Age
    16 to 18
    Challenge level
    1 out of 3

    Use functions to create minimalist versions of works of art.