Operations on Functions

The Lesson Activities will help you meet these educational goals:

  • Mathematical Practices—You will use mathematics to model real-world situations.
  • STEM—You will apply mathematical knowledge to analyze real-world situations.
  • 21stCentury Skills—You will use critical-thinking and problem-solving skills.

Directions

Save this document before beginning the lesson and keep the document open for reference during the lesson. Type your answers directly in this document for all activities.

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Self-Checked Activities

Read the instructions for the following activities and type in your responses. At the end of the lesson, click the link to open the Student Answer Sheet. Use the answers or sample responses to evaluate your own work.

  1. Adding and Subtracting Functions

Two neighboring towns, NashTown and BayTown, were surveyed, and their populations were found to be and (in thousands), respectively, where x is the number of years since the towns were founded. (Assume that both towns were founded at the same time.)

  1. Find the function that gives the total population of both towns.

Sample answer:

Let f(x) be the population of NashTown and g(x) be the population of Bay Town:

and

The total population of both towns is given by

  1. Find the function that gives the difference of the populations of NashTown and BayTown.

Sample answer:

The difference of the populations of Nash Town and Bay Town is given by

  1. Multiplying and Dividing Functions

The price of a particular product of a certain company varies with time (t in days) and is given by the function Assume that the revenue generated from the product is exactly equal to the product’s price multiplied by the number of units sold and that the price has no effect on the demand for the product.

  1. If the revenue generated from January to June is given by what function gives the quantity produced?

Sample answer:

Let be the quantity produced in time t.

revenue = price × quantity

  1. If unit sales of the product for the period July to December is given by what function gives the revenue generated?

Sample answer:

Let be the quantity produced in time t.

revenue = price × quantity

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