7.1.1 Noticing New Patterns of Change

Algebra 17.1.1 Noticing New Patterns of Change

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7.1.1 • Noticing New Patterns of Change

Warm Up

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 $x$ -values are $1$ , $2$ , $3$ , $4$ , and $5$ in all three tables.
In the first two tables, the $y$ -values increase, while in the third table, they increase and then decrease.
The $y$ -values in the first table are all multiples of $5$ , and they grow linearly. In the second table, the $y$ -values grow by a factor of $2$ each time $x$ increases by $1$ . In the third table, there isn’t an obvious pattern in how the $y$ -values change.

Things you may wonder:

Is there a rule for the relationship in the third table?
Will the $y$ -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?

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- Authors: Lynn Marecek, MaryAnne Anthony-Smith, Andrea Honeycutt Mathis, Jay Abramson, Sharon North, Amy Baldwin, Alyssa Howell
- Publisher/website: OpenStax
- Book title: Algebra 1
- Publication date: Jun 4, 2025
- Location: Houston, Texas
- Book URL: https://openstax.org/books/algebra-1/pages/about-this-course
- Section URL: https://openstax.org/books/algebra-1/pages/7-1-1-noticing-new-patterns-of-change

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