Constructing a piecewise model
Write a separate rule for each part of a situation’s domain.
- Identify where the rule changes.
- Use inequalities that include the boundary exactly once.
- For a charge above a threshold, charge the extra rate only on the amount above that threshold.
Example
A delivery charge
Write a piecewise function to model the cost. Delivery costs $6 for a positive weight up to 3 pounds, then $2 per pound above 3 pounds.
Your turn
5 practice questions0 of 5 answers checked
A delivery costs $5 for a positive weight up to 2 pounds. Above this, add $3 per pound over 2 pounds. Write
Check answer
A delivery costs $8 for a positive weight up to 4 pounds. Above this, add $2 per pound over 4 pounds. Write
Check answer
A delivery costs $10 for a positive weight up to 5 pounds. Above this, add $4 per pound over 5 pounds. Write
Check answer
A delivery costs $4 for a positive weight up to 1 pounds. Above this, add $2 per pound over 1 pounds. Write
Check answer
A delivery costs $12 for a positive weight up to 6 pounds. Above this, add $3 per pound over 6 pounds. Write
Check answer
A delivery costs $5 for a positive weight up to 2 pounds. Above this, add $3 per pound over 2 pounds. Write
A delivery costs $8 for a positive weight up to 4 pounds. Above this, add $2 per pound over 4 pounds. Write
A delivery costs $10 for a positive weight up to 5 pounds. Above this, add $4 per pound over 5 pounds. Write
A delivery costs $4 for a positive weight up to 1 pounds. Above this, add $2 per pound over 1 pounds. Write
A delivery costs $12 for a positive weight up to 6 pounds. Above this, add $3 per pound over 6 pounds. Write