A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.

A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.

A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.

A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.

A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.

A graph of $f$ is drawn. Graph of a transformed version of $f$ is to be sketched, by dragging various points around.

Horizontal and vertical shifts and scales of a random cubic spline

of a random cubic spline

of a random cubic spline

of a random cubic spline

of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

Horizontal translation to the left of some function f(x)

Given the graphs of two functions $f$ and $g$ can you sketch the graph of $f+g$?

Given the graphs of two functions $f$ and $g$ can you sketch the graph of $f+g$?

Given the graphs of two functions $f$ and $g$ can you sketch the graph of $f+g$?

Given the graphs of two functions $f$ and $g$ can you sketch the graph of $f+g$?

of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

Horizontal and vertical shifts and scales of a random cubic spline

Asking users to input coefficients of a system of diff equations so that the phase space is a centre. All systems input by the user are graphed together with immediate feedback. Also included in the Steps are the graphs of the solutions for $x(t),\; y(t);\; x(0)=-5,\;y(0)=5.$

Nature of fixed points of a 2D dynamical system.

These examples are either centres or spirals.

Asking users to input coefficients of a system of diff equations so that the phase space is a centre. All systems input by the user are graphed together with immediate feedback. Also included in the Steps are the graphs of the solutions for $x(t),\; y(t);\; x(0)=-5,\;y(0)=5.$

Asking users to input coefficients of a system of diff equations so that the phase space is a stable spiral. All systems input by the user are graphed together with immediate feedback. Also included in the Steps are the graphs of the solutions for $x(t),\; y(t);\; x(0)=-5,\;y(0)=5.$

Asking users to input coefficients of a system of diff equations so that the phase space is a saddle. All systems input by the user are graphed together with immediate feedback. Also included in the Steps are the graphs of the solutions for $x(t),\; y(t);\; x(0)=-5,\;y(0)=5.$

of a random cubic spline