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Cogito

Integrated Math 3 · Chapter 8 · Lesson 3

Practice Worksheet

Piecewise Models and Systems

When one rule does not cover everything.

12 problems · about 21 minutes · F-IF.C.7, A-REI.C.6

NameDate

Figure — use these to answer the problems

Two plans are two lines. Where they cross is the usage at which the cheaper plan changes.
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y = 2x + 3
Cost per unit2
Fixed fee3
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. 4u + 50 = 6u + 30. What is u?

    Answer

  2. What does the intersection of two cost models represent?

    • The usage at which both options cost the same.
    • The cheapest possible cost.

  3. 3u + 20 = 5u + 10. What is u?

    Answer

  4. C = 4u + 10 at u = 10. What is C?

    Answer

  5. Below the break-even point, which plan is cheaper here? 1 the lower fixed fee, 2 the higher.

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. A piecewise rule changes at x = 4. Is 4 a break point? 1 yes, 0 no.

    Answer

  2. Both pieces agree at the boundary. Is the graph continuous there? 1 yes, 0 no.

    Answer

  3. C = 2u + 30 at u = 25. What is C?

    Answer

Stretch Yourself

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

4 problems

  1. Put the comparison process in order.

    Write 1 to 4 in the boxes to put these in order.

    • Write a function for each option.
    • Set the two equal.
    • Solve for the break-even usage.
    • State which option wins on each side of it.

  2. 5u + 40 = 9u + 20. What is u?

    Answer

  3. The Break-Even

    2u + 30 = 4u + 10. What is u?

    Answer

  4. The Cost

    Plan A is C = 2u + 30. What is the cost at 10 units, in dollars?

    Answerdollars