Functions
Section 2-5
| Activity Name | Activity Description |
|---|---|
| Function Machine | Students enter an input value (x) to the applet and use the corresponding output value ( y = f[x] ) to determine the form of simple algebraic functions. |
| Linear Function Machine | Students enter an input value (x) to the applet and use the corresponding output value ( y = f[x] ) to determine the slope and intercept of linear functions. |
| Positive Linear Function Machine | Students enter an input value (x) to the applet and use the corresponding output value ( y = f[x] ) to determine positive values for the slope and intercept of linear functions. |
| Vertical Line Test | The applet generates and plots a sequence of random ordered pairs on a coordinate plane. From the graph, students select points which are connected in sequence by line segments, either generating a function with one-to-one correspondence or a non-function that fails to meet the 'vertical line test' criterion. |
| Sequencer | Students input parameters (starting number, multiplier, addend) to generate number patterns in arithmetic and geometric sequences. The applet plots the sequence as a linear function. |
| Caesar Cipher | Students input parameters to create coded messages using an affine cipher. Discussion can focus on the linear function used to create the cipher. |
| Caesar Cipher II | Students determine the parameters for an affine cipher used by the applet to generate 'secret code' versions of student messages. Discussion can focus on the linear function used to create the cipher. |
| Caesar Cipher III | Students decode and determine parameters for an affine cipher message generated by the applet. Discussion can focus on the linear function used to create the cipher and on the related function used to decode the cipher. |
| Graph Sketcher | Students input y = f(x) style formulas to create graphs of functions on the coordinate plane. The applet is similar to a graphing calculator. |
| Graphit | Students input both y = f(x) style formulas and sets of ordered pairs to create graphs of functions on the same coordinate plane. The applet is similar to a graphing calculator. |
| Possible or Not? | The applet supplies a sequence of coordinate graph curve plots that can be used to drill students on the identification of curves as 'functions'. |
| The 2 Variable Function Pump | Students input a pair of complex numbers as ordered pairs. The applet then plots successive points on a real graph corresponding to the iterative complex function underlying the Julia and Mandlebrot sets. |
| Julia Sets | Students input a complex starting constant (c) as an ordered real number pair to investigate the Julia Sets associated with the iterative function f(z)=z2 + c. The applet draws the corresponding fractal pattern for each given value of c. |
| The Mandelbrot Set | Students use a click and zoom graphical interface to investigate the relationships between geometric fractal patterns of the Mandelbrot set and the family of Julia sets. The Mandelbrot Set is the set of all functions of the form f(z)=z2 + c for all complex numbers, c. |
