This document discusses three methods for comparing functions using inequalities: 1) Compare functions visually using different colors or styles, 2) Analyze the difference function by graphing it to see where it is above the x-axis, and 3) Analyze the quotient function by graphing it to identify where one quotient is greater than the other, corresponding to where one function is greater than the other. The document also covers using the quadratic formula with inequalities and applying these methods to basic functions and word problems.

1. Inequalities of Combined FunctionsBy: Sasha Harris, Scott Rideout, Courtney Ritchey, Chris Armstrong, Julia Meyers.

3. Method 1:Method 1: Compare the functions visuallyUsing different colors or line styles when comparing functions will show which areas of one function are greater than the other.

4. Method 2 / Method 3:Method 2: Analyze the difference functionSubtracting two functions and seeing where the graph of the difference is above the x-axis will also illustrate where one function is greater than the other Method 3: Analyze the quotient functionThe functions f(x) and g(x) can also be compared by analyzing their quotient. Graphing the quotient will identify the intervals where one quotient is greater than the other, which corresponds to where f(x) > g(x)

5. What you Should Have LearnedHow to solve a combined function using an inequality ( with each method)

6. How to use the Quadratic formula with inequalities

7. Application / word problems

8. Basic functions: The End!Questions?