Question

Please help and answer in simple terms

Compare and contrast exponential and linear functions using both graphs and tables. How would you determine if a function is linear or exponential by looking only at a table?

Answer 1

If the same number is being added to y, then the function has a constant change and is linear. If the y value is increasing or decreasing by a certain percent, then the function is exponential.

Explanation:

I'll give you an example:

We have 2 functions as tables.

The first table:

X. Y.

1 6

2 9

3 1

4 40

And the second table:

X. Y.

1 2

2 4

3 6

4 8

Which one is linear, and which one is exponential?

The first table is exponential, while the second table is linear.

Why?

The first table's difference of Y1 & Y2 is 3, Y2 & Y3 is 8, Y3 & Y4 is 39. This means that Y does not increase at a constant rate, as X increses by 1. Therefore, this function is exponential.

The second table's difference between Y1 & Y2, Y2 & Y3, Y3 & Y4 is 2. Therefore, 2 is Y's constant change. Since the second table has a constant change, this function is linear.