Figuring out if a function is linear or nonlinear using tables can be really fun! 🌟 You’ll see how easy it is to understand what these functions mean by looking at tables.

1. Constant Rate of Change:

• For linear functions, the difference between the $y$-values (the results) stays the same when the $x$-values (the inputs) change. This steady difference is called the slope.
• On the other hand, for nonlinear functions, the changes in $y$-values are not the same. You’ll notice different differences from one $y$-value to the next!

2. Example:

• Let’s look at this table:

| $x$ | $y$ | |-----|-----| | 1 | 2 | | 2 | 4 | | 3 | 6 |

• In this table, the $y$-values go up by 2 each time ($2, 4, 6$). This tells us it’s a linear function.

3. Nonlinear Example:

| $x$ | $y$ | |-----|-----| | 1 | 1 | | 2 | 4 | | 3 | 9 |

• Here, the differences (3, 5) change, which tells us it’s a nonlinear function!

By studying these tables, you’re like detectives solving the mystery of functions! Keep on exploring and have a blast learning about algebra! 🎉