Recognize functions from verbal descriptions (example 2) | Algebra II | Khan Academy

TL;DR

The dollar amount of an order cannot be represented as a function of shipping costs due to multiple potential outputs for a given shipping cost.

Transcript

Jada is ordering Mother's Day gifts online. The shipping costs are based on the dollar amount of the order. For orders less than $20, shipping costs $4. For orders $20 or more, shipping is $7. Can the dollar amount of the order be represented as a function of shipping costs? So they're saying, can the dollar amount of the order-- so can the amount ... Read More

Key Insights

• 🪈 The dollar amount of an order cannot be represented as a function of shipping costs due to multiple potential outputs.
• 📦 There are only two possible shipping costs: $4 or $7.
• 🪈 For a shipping cost of $4, the amount of the order can be any value less than $20.
• 🪈 When the shipping cost is $7, the amount of the order must be $20 or more.
• ⚾ There is an infinite number of potential output values for the amount of the order based on a valid shipping cost.

Questions & Answers

Q: Can the dollar amount of an order be represented as a function of shipping costs?

No, because for a valid shipping cost, there can be many potential outputs for the dollar amount of the order. It is not possible to determine the exact output based solely on the shipping cost.

Q: What are the possible inputs for the shipping costs?

The possible inputs for the shipping costs are $4 and $7. These are the two available options for shipping cost.

Q: If the shipping cost is $4, what is the possible range for the amount of the order?

If the shipping cost is $4, the amount of the order can be any value less than $20. It can range from $1 to $19.99.

Q: What is the range for the amount of the order if the shipping cost is $7?

If the shipping cost is $7, the amount of the order must be $20 or more. It can vary from $20 to any higher amount, including infinite possibilities.

Summary & Key Takeaways

• Jada is ordering Mother's Day gifts online, and the shipping costs are based on the dollar amount of the order.

• For orders less than $20, shipping costs $4. For orders $20 or more, shipping is $7.

• To represent the dollar amount of the order as a function, there should be exactly one output for a given shipping cost, but in this case, there are multiple potential outputs.