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Lesson 9

Increasing and Decreasing Functions

Let’s look at what a graph does based on a situation.

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 \(f(x) = 5 - 2x\).
1. \(f(3)\ \underline{\hspace{.5in}}\ f(5)\)
2. \(f(\text{-}3)\ \underline{\hspace{.5in}}\ f(\text{-}4)\)
3. \(f(\text{-}1)\ \underline{\hspace{.5in}}\ f(1)\)

Describe \(f(x)\) and \(g(x)\) with a situation that could fit the given graphs. Explain your reasoning.

$Two graphs \(f\) and \(g\) on a grid. Graphs \(f\) and \(g\) cross. Graph \(f\) starts at the origin.$
$Graphs \(f\) and \(g\). Graph \(f\) starts at the origin. Graph \(g\) starts at x axis.$
$Graphs of \(f\) and \(g\). Graph \(f\) starts at origin. Graph \(g\) starts at y axis.$
$Graphs \(f\) and \(g\). Both graphs go from the y axis to the x axis.$

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.