Math 10C Module 6: Lesson 1

Module 6: Linear Equations

Lesson 1: Function Notation

Focus

This shows a photo collage. A photo shows a man posing with a guitar game controller. A second photo shows a mother and daughter singing on microphones while the father and son look on.

man: © Scott Griessel/20972268/Fotolia; family: Getty Images/Comstock/Thinkstock

If you like to play music and you also like video games, you may enjoy playing a music video game. These games allow you to play popular music on game controllers designed to look and feel like real musical instruments including guitars and drum kits. Some of these games also come packaged with a microphone for singing along. Whether playing an instrument or singing a solo, players attempt to match the song notes that scroll on the video screen.

Every time you finish playing a song, the game displays your score as a percentage of the total number of notes that were played correctly. Reviewers of such games have indicated that they are entertaining, challenging, and fairly realistic. All video games are designed to allow the user to provide inputs into the game that result in output action on-screen.

The success of music video games comes from the fact that the games give the user a wider variety of inputs and combinations of inputs that result in an experience that closely approximates playing an otherwise complex song on a real instrument. For example, each drum pad emits a different sound, whether it is that of a bass drum, a cymbal, or tom. When a guitar is strummed, the tone that is heard depends on the fret buttons that are pressed. Inputs can be a single tap on a drum pad or simultaneous taps on two drum pads at different rates.

In the previous module you began your study of functions. You learned that a function is a relation between an input value (often called x) and the related output value (often called y). Each function has its own rule, and there is only one possible output value for any input value.

In this lesson you will learn a new way to represent a linear function known as function notation. In any function, there is a single output for every input. Function notation emphasizes the input/output property of functions.

Outcomes

At the end of this lesson, you will be able to

  • express the equation of a linear function in two variables using function notation

  • express an equation given in function notation as a linear function in two variables

  • determine the related range value, given a domain value for a linear function; e.g., if f(x) = 3x − 2, determine f(−1)

  • determine the related domain value, given a range value for a linear function; e.g., if g(t) = 7 + t, determine t so that g(t) = 15

  • sketch the graph of a linear function expressed in function notation

Lesson Questions

  • How do you sketch the graph of a linear function expressed in function notation?

  • Why are different types of notation used in mathematics?

Lesson Completion and Assessment

As you work through each lesson, complete all the questions and learning activities in your binder using paper and pencil, clearly labeling your work (they refer to this as your course folder). These include the Are you Ready, Try This, Share and Self Check questions. Check your work if answers are provided. Remember that these questions provide you with the practice and feedback that you need to successfully complete this course.
Once you have completed all of the learning activities, take the Lesson Quiz. This is the assessment for each lesson and is located under the Activities block on the left in moodle or under the Assess tab.


** Note – Share questions may have to be done on your own depending on your learning situation**

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