Lesson 9
Increasing and Decreasing Functions
 Let’s look at what a graph does based on a situation.
9.1: Comparing Values
For each pair of numbers, write \(=,<\), or \(>\) in the blank to make a true equation or inequality. Be prepared to share your reasoning.
 6 \(\underline{\hspace{.5in}}\) 9
 \(\frac{7}{3}\ \underline{\hspace{.5in}}\ \frac{13}{6}\)
 5.2 \(\underline{\hspace{.5in}}\ \frac{53}{11}\)
 \(5 (3  6)\ \underline{\hspace{.5in}}\ 15  6\)
 Let \(f(x) = 5  2x\).
 \(f(3)\ \underline{\hspace{.5in}}\ f(5)\)
 \(f(\text{}3)\ \underline{\hspace{.5in}}\ f(\text{}4)\)
 \(f(\text{}1)\ \underline{\hspace{.5in}}\ f(1)\)
9.2: What Could It Be?
Describe \(f(x)\) and \(g(x)\) with a situation that could fit the given graphs. Explain your reasoning.
9.3: Cities, Towns, and Villages
Draw an example of a graph that shows two functions as they are described. Make sure to label the functions.

The population of 2 cities as functions of time so that city A always has more people than city B.

The population of 2 towns as functions of time so that town A is larger to start, but then town B gets larger.

The population of 2 villages as functions of time so that village A has a steady population and village B has a population that is initially large, but decreases.