Graph sketching

problem
Speeding up, slowing down

Age

11 to 14

Challenge level

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its speed at each stage.
problem
How far does it move?

Age

11 to 14

Challenge level

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects the distance it travels at each stage.
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
Slide

Age

16 to 18

Challenge level

This function involves absolute values. To find the slope on the slide use different equations to define the function in different parts of its domain.
problem
Polar flower

Age

16 to 18

Challenge level

This polar equation is a quadratic. Plot the graph given by each factor to draw the flower.
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
Area L

Age

16 to 18

Challenge level

By sketching a graph of a continuous increasing function, can you prove a useful result about integrals?
problem
Exploring cubic functions

Age

14 to 18

Challenge level

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