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

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.

\(y = 3x  2\)
\(x\) \(y\) 1 3 2 
\(y = 52x\)
\(x\) \(y\) 0 3 5 
\(y = \frac{1}{2}x + 2\)
\(x\) \(y\) 4 3 6 
\(x\) \(y = 2x  10\) 3 7 8
5.3: Function Finder

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

\(x\) \(y\) 1 3 2 5 3 7 5 11 
\(x\) \(y\) 2 0 0 1 2 2 4 3 
\(x\) \(y\) 2 14 1 12 1 8 2 6

 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.
 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.