Graph sketching

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.

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

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?

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.

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

Plot the graph of x^y = y^x in the first quadrant and explain its properties.

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

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

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.