Operations on Functions

What operations on functions should learners be able to perform by the end of the lesson?

What is the toll fee during the day?

What is the toll fee at night?

What is the admission fee for visitors aged 2 years or younger?

What is the admission fee for visitors older than 2 years?

How much does a parking lot charge for the first hour?

How much does the parking lot charge for each additional hour?

What is the flat rate charged by the water utility company for up to 500 gallons?

What is the additional charge per gallon for water used beyond 500 gallons?

If Jen stays for 4 hours in the parking lot, what is her total charge?

If Cara stays for 7 hours in the parking lot, what is her total charge?

If Jen travels for 500 gallons of water, what is her total cost?

If Cara travels for 600 gallons of water, what is her total cost?

Operations on Functions

Addition, subtraction, multiplication, division, and composition are the main operations performed on functions.
Understanding how to manipulate functions is essential for problem-solving in mathematics.

Toll Road Fees

Daytime toll fee: $1 (6 AM to 6 PM).
Nighttime toll fee: $2 (6 PM to 6 AM).
Function representation: Let 𝐶(𝑥) represent the toll fee, where 𝑥 is the hour (0-23).

Zoo Admission Fees

Admission fee for children aged 2 years or younger: $3.
Admission fee for visitors older than 2 years: $7.
Function representation: Let 𝐶(𝑥) represent the admission fee, where 𝑥 is the visitor's age.

Parking Lot Charges

Cost for the first hour: $5.
Additional hours cost: $3 per hour.
Function representation: Let 𝐶(𝑥) represent the total cost, where 𝑥 is the number of hours parked.
Example scenarios:
- Jen parks for 4 hours.
- Cara parks for 7 hours.

Water Utility Costs

Flat rate for up to 500 gallons: $30.
Additional charge for usage over 500 gallons: $0.05 for each gallon beyond 500.
Function representation: Let 𝐶(𝑥) represent the total cost, where 𝑥 is the number of gallons used.
Example scenarios:
- Jen uses 500 gallons, incurring a total fee of $30.
- Cara uses 600 gallons, incurring an additional charge for the excess.

Conclusion

These examples illustrate how to construct functions based on real-world scenarios and apply operational functions to derive costs and fees.

This quiz focuses on performing various operations on functions, including addition, subtraction, multiplication, division, and composition. Students will learn how to navigate through examples and practical applications of these operations, such as calculating toll fees based on time of day. Get ready to test your understanding of function operations!