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.

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

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.

    Blank coordinate grid, origin O. Horizontal axis 0 to 20, by 2s, time, years. Vertical axis 0 to 200, by 20s, population, in thousands.
  2. The population of 2 towns as functions of time so that town A is larger to start, but then town B gets larger.

    Blank coordinate grid, origin O. Horizontal axis 0 to 20, by 2s, time, years. Vertical axis 0 to 200, by 20s, population, in thousands.
  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.

    Blank coordinate grid, origin O. Horizontal axis 0 to 20, by 2s, time, years. Vertical axis 0 to 200, by 20s, population, in thousands.

Summary