Lesson 5

Function Representations

  • Let’s examine different representations of functions.

5.1: Notice and Wonder: Representing Functions

What do you notice? What do you wonder?

\(f(x) = \frac{2}{3}x - 1\)

Line on coordinate grid, origin O. Both axes from negative 4 to 4, by 2's. Line passes through negative 3 comma negative 3, 0 comma negative 1, and 3 comma 1.
\(x\) \(y\)
-1 \(\text{-}\frac{5}{3}\)
0 -1
1 \(\text{-}\frac{1}{3}\)
2 \(\frac{1}{3}\)
3 1

5.2: A Seat at the Tables

Use the equations to complete the tables.

  1. \(y = 3x - 2\)

    \(x\) \(y\)
    1  
    3  
    -2  
  2. \(y = 5-2x\)
    \(x\) \(y\)
    0  
    3  
    5  

     

  3. \(y = \frac{1}{2}x + 2\)
    \(x\) \(y\)
    -4  
    3  
    6  

     

  4. \(x\) \(y = 2x - 10\)
    3  
    7  
    -8  

     

5.3: Function Finder

  1. Use the values in the table to graph a possible function that would have the values in the table.

    1. \(x\) \(y\)
      1 3
      2 5
      3 7
      5 11
      A blank coordinate grid. The horizontal axis, x, scale from negative 15 to 15 by 1s. The vertical axis, y, scale from negative 15 to 15, by 1s.
    2. \(x\) \(y\)
      -2 0
      0 1
      2 2
      4 3
      A blank coordinate grid. The horizontal axis, x, scale from negative 15 to 15 by 1s. The vertical axis, y, scale from negative 15 to 15, by 1s.
    3. \(x\) \(y\)
      -2 14
      -1 12
      1 8
      2 6
      A blank coordinate grid. The horizontal axis, x, scale from negative 15 to 15 by 1s. The vertical axis, y, scale from negative 15 to 15, by 1s.
  2. For each of the tables and graphs, write a linear equation (like \(y = ax + b\)) so that the table can be created from the equation.
  3. Invent your own linear equation. Then, create a table or graph, including at least 4 points, to trade with your partner. After getting your partner’s table or graph, guess the equation they invented.

Summary