# Gaussian Function

Gaussian
functions of the form
^{ -(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.
## Tutorial1 - 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 Questions2 - 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. ## More References and LinksApplications, Graphs, Domain and Range of Functions |