# 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.

1. -6 $$\underline{\hspace{.5in}}$$ -9
2. $$\frac{7}{3}\ \underline{\hspace{.5in}}\ \frac{13}{6}$$
3. 5.2 $$\underline{\hspace{.5in}}\ \frac{53}{11}$$
4. $$5 (3 - 6)\ \underline{\hspace{.5in}}\ 15 - 6$$
5. Let $$f(x) = 5 - 2x$$.
1. $$f(3)\ \underline{\hspace{.5in}}\ f(5)$$
2. $$f(\text{-}3)\ \underline{\hspace{.5in}}\ f(\text{-}4)$$
3. $$f(\text{-}1)\ \underline{\hspace{.5in}}\ f(1)$$

### 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.

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

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

3. 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.