# Gaussian Function

Gaussian functions of the form

f(x) = a e -(x - b) 2 /c

and the properties of their graphs are explored.

Parameters a, b and c defining the gaussian function are changed and their effects analyzed.

## Tutorial

 a = 1 -10+10 b = 0 -10+10 c = 1 1+10
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1 - click on the button above "draw" to start. The graph of the gaussian function is displayed.

2 - Use the sliders to set parameters b to 0 and c to 1 and change parameter a. What happens to the graph?

3 - Now set parameters a to 1 and c to 1 and change parameter b. What happens to the graph? Explain analytically.

4 - Set parameters a to 1 and b to 0 and change parameter c. What happens to the graph when c takes small values? What happens to the graph when c takes larger values?

## Answers to the Above Questions

2 - The graph expands vertically as a increases. The y values of the points making the graph are multiplied by the value of a.

3 - As b increases, the graph is shifted to the right. As b decreases the graph is shifted to the left.

4 - As c is made small, the graph shrinks horizontally. As c is made large, the graph expands horizontally.