MATH112 graph functions

This discussion re-visits the concept of a function. You will explore the online graphing tool Desmos and graph algebraic functions.

1. Access the attached Desmos User Guide and review all sections except for Regressions.
2. Use Desmos (https://www.desmos.com/calculator) to graph three assigned functions, as follows: Start by graphing either y = 1/x or y = 1/x^2 and modify that function to create the graphs of three other algebraic functions with the following properties:

a. one vertical asymptote (no horizontal asymptote)

b. one horizontal and two vertical asymptotes

c. one horizontal asymptote (no vertical asymptote). Ensure that the entire function 2c is in the positive halfplane.

3. Using the graph of each function, state the domain and range, and write the equations of the horizontal and vertical asymptotes.

4. In five to ten sentences, explain your rationale for determining the domain, the range, and the asymptotes from the graph. What ideas have you studied previously that were useful in the analysis?