2.6.A.1Concept
Two variables in a data set that demonstrate a slightly changing rate of change can be modeled by linear, quadratic, and exponential functions.
ExampleWhich type does each table suggest?1 / 3
Three tables give values at equally spaced inputs. Use differences, second differences, and ratios to decide whether each is linear, quadratic, or exponential.
| x | 0 | 1 | 2 | 3 | 4 |
| f(x) | 5 | 9 | 13 | 17 | 21 |
| g(x) | 3 | 5 | 9 | 15 | 23 |
| h(x) | 2 | 6 | 18 | 54 | 162 |
Try it on paper first, then reveal each step to check your work.
Step 1 — Look at f
The differences are 4, 4, 4, 4. A constant first difference means f is linear: f(x) = 4x + 5.