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Cogito

Integrated Math 3 · Chapter 8 · Lesson 1

Practice Worksheet

Choosing a Function Model

Which family does the data want?

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

NameDate

Figure — use these to answer the problems

Compare this shape against a parabola and a line. Recognising the shape is most of choosing a model.
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y = 1 · 2^x + 0
a1
b2
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. 4, 9, 14, 19. Which family? 1 linear, 2 quadratic, 3 exponential.

    Answer

  2. What identifies a quadratic from a table?

    • Constant second differences.
    • Constant ratios.

  3. 3, 7, 11, 15. Which family? 1 linear, 2 quadratic, 3 exponential.

    Answer

  4. 2, 6, 18, 54. Which family? 1, 2 or 3?

    Answer

  5. 1, 4, 9, 16. First differences are 3, 5, 7. What is the second difference?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Daily temperature over a year. Which family? 1 linear, 2 trigonometric.

    Answer

  2. A projectile height against time. 1 linear, 2 quadratic.

    Answer

  3. Total cost at a fixed price per item. 1 linear, 2 exponential.

    Answer

Stretch Yourself

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

4 problems

  1. Match each pattern with the family it identifies.

    Draw a line from each item on the left to its match on the right.

    • Constant first differences
    • Constant second differences
    • Constant ratios
    • Linear
    • Quadratic
    • Exponential

  2. 5, 10, 20, 40. Which family? 1 linear, 2 quadratic, 3 exponential.

    Answer

  3. The Table

    1, 4, 9, 16. Which family? 1 linear, 2 quadratic, 3 exponential.

    Answer

  4. The Growth

    A balance growing 5% a year. Which family? 1 linear, 2 quadratic, 3 exponential.

    Answer