Choosing a Function Model

Which family does the data want?

12 problems · about 21 minutes · F-LE.A.1, F-BF.A.1

What this lesson teaches

The student selects an appropriate function family for given data or context.

Constant first differences mean linear, second differences quadratic, ratios exponential.
Repeating data needs a trigonometric model.
Context often names the family before any table is examined.

Straightforward practice. Get the method working first.

5 problems

4, 9, 14, 19. Which family? 1 linear, 2 quadratic, 3 exponential.
Answer 1
Why Linear.
What identifies a quadratic from a table?
Answer Constant second differences.
Why The second differences.
3, 7, 11, 15. Which family? 1 linear, 2 quadratic, 3 exponential.
Answer 1
Why Constant first differences.
2, 6, 18, 54. Which family? 1, 2 or 3?
Answer 3
Why Constant ratio.
1, 4, 9, 16. First differences are 3, 5, 7. What is the second difference?
Answer 2
Why 5 − 3.

The same ideas with more to keep track of.

3 problems

Daily temperature over a year. Which family? 1 linear, 2 trigonometric.
Answer 2
Why It repeats yearly.
A projectile height against time. 1 linear, 2 quadratic.
Answer 2
Why Gravity gives a parabola.
Total cost at a fixed price per item. 1 linear, 2 exponential.
Answer 1
Why A fixed amount per unit.

Mixed problems. Work out what kind of question it is before you start.

4 problems

Match each pattern with the family it identifies.
Answer Constant first differences → Linear; Constant second differences → Quadratic; Constant ratios → Exponential
Why Each test identifies exactly one family.
5, 10, 20, 40. Which family? 1 linear, 2 quadratic, 3 exponential.
Answer 3
Why Constant ratio of 2.
The Table: 1, 4, 9, 16. Which family? 1 linear, 2 quadratic, 3 exponential.
Answer 2
Why Quadratic.
The Growth: A balance growing 5% a year. Which family? 1 linear, 2 quadratic, 3 exponential.
Answer 3
Why Exponential.