Warm Up
1.
Look at the patterns in the three tables. What do you notice? What do you wonder?
| x | y |
| 1 | 0 |
| 2 | 5 |
| 3 | 10 |
| 4 | 15 |
| 5 | 20 |
| x | y |
| 1 | 3 |
| 2 | 6 |
| 3 | 12 |
| 4 | 24 |
| 5 | 48 |
| x | y |
| 1 | 8 |
| 2 | 11 |
| 3 | 10 |
| 4 | 5 |
| 5 | -4 |
Compare your answers:
Things you may notice:
- The -values are , , , , and in all three tables.
- In the first two tables, the -values increase, while in the third table, they increase and then decrease.
- The -values in the first table are all multiples of , and they grow linearly. In the second table, the -values grow by a factor of each time increases by . In the third table, there isn’t an obvious pattern in how the -values change.
Things you may wonder:
- Is there a rule for the relationship in the third table?
- Will the -values in the third table continue to decrease, or will they increase again at some point?
- What would the third relationship look like if graphed?