We take that great old problem of the inventor of chess and the ruler of India and use it to see how powers of 2 grow in size. We start out with a chessboard and look at doubling each successive number. Then we seek a method of representing this doubling in a formula and introduce exponents and powers of 2. We ask you what kind of rule would you suggest that would keep your head and please the ruler?
Category: Functions
Sine Function
Spreadsheets are not limited to algebraic functions, they can also display trigonometric functions. We are modeling the sine function, but you can try any of the trig functions by going to the Formulas menu and choosing it. We have the 3 most significant parameters of the sine function, to control the amplitude, frequency and phase. We also introduce radian measure which is the natural quantity for trig functions.
Polynomial Functions
Polynomial functions are not limited to the highest term and while that term is most important in determining the shape of its graph, additional terms play a role. Try out additional terms to see how they affect the shapes of the graph. Focus on the patterns!
Power Functions
Adding an exponent, sometimes referred to as a ‘power’, to the input variable of a linear function that passes through the origin creates a power function. Changing the parameters of these functions reveal some important and interesting patterns.
Quadratic Functions
What does each of the coefficients do? How does it change the graph of the parabola. What does a do, what does c do and a question still rarely asked, what does changing b do to change the graph. To see what b does more clearly we have you add a graph of the linear portion of the quadratic function to the picture so that you can see the pattern it makes and it causes the parabola to make. Quadratic functions give you a chance to really and experiment with this very important family of functions.