**Transformations of Functions**

Examining how graphical transformations of parent functions are determined by changes to the function rule.

**Ellipses and Hyperbolas as Conic Sections**

Examining how the foci coordinates and the distance sum/difference create ellipses and hyperbolas.

**Unit Circle and Its Graphs
**

Examining how the geometric definitions of the trigonometric functions on the unit circle relate to each other and their graphs.

**Exploring Polar Graphs**

Examining how graphs of r versus theta are constructed.

**Exploring Complex Roots**

Examining the how complex numbers generate the geometry of their roots.

**Derivatives of Inverses**

Examining how derivatives of points of inverse functions symmetric across y = x are reciprocals of each other.

**Tangent Line Approximation**

A project that examines how tangent lines can approximate function values and what parameters affect the accuracy of the approximation.

**Newton's Method**

Examining the process through which Newton's method finds zeros of functions and how the initial guess determines accuracy and convergence.

**Slope Fields**

Examining how slope fields provide a visualization of the behavior of the solution to a differential equation.

**Euler's Method**

Examining how Euler's method produces approximate solutions to an initial value problem.

**Right Riemann Sums**

A project that examines how right Riemann sums approximate the area under a curve within a finite interval.

**Investigating Series**

Examining how terms, partial sums, and remainder all tie in to the concepts of convergence and divergence.

**Investigating Taylor Polynomials**

Examining how various Taylor polynomials converge to their respective functions, including looking at finite intervals of convergence.

**Derivatives of Parametric Curves**

Examining how derivatives and tangent lines to parametric curves work.

**Polar Derivatives**

Exploring the meaning of the various derivatives of polar functions with respects to theta, x, and y.

**Polar Area**

Investigating how a series of circular sectors limits to the area enclosed by a polar curve.

**3D Graphing**

A modification of a user's 3D Graphing interface.