# 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.

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
2. $$x$$ $$y$$
-2 0
0 1
2 2
4 3
3. $$x$$ $$y$$
-2 14
-1 12
1 8
2 6
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.