1 / 10

Understanding Composite Functions in Precalculus

In today's precalculus lesson, we'll explore the concept of composite functions. We'll start with a warm greeting before diving into the lab and homework assignments. Learn how to graph functions using time as a domain, where we evaluate ( f(x(t)) ) to visualize y-values based on x-values over time. We'll simplify this to understand operations like "f composed with x" and apply these concepts to real-life examples. Homework will focus on evaluating function compositions both algebraically and graphically. Remember to tidy up before leaving class!

alcina
Télécharger la présentation

Understanding Composite Functions in Precalculus

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. GBK PrecalculusJordan Johnson

  2. Today’s agenda • Greetings • Lesson: Composite Functions • Lab • Homework • Clean-up

  3. Graphing on the computer • For animations, the domain is time. • Suppose we get x-values from a function x(t),and want to graph y-values from a function f(x). • …so we really have f(x(t)). x f time x-values y-values

  4. Going further • Could think of it as one operation: x then f time y-values x f time x-values y-values

  5. Going further • Could think of it as one operation: f ◦ x time y-values x f time x-values y-values “f composed with x”, or “f composition x”, or “f following x”, or just plain “f of x”

  6. Going further • More mundanely: dry ◦ wash dirty dishes clean dry dishes wash dry dirty dishes clean wet dishes clean dry dishes

  7. Next steps • Evaluate the composition of two functions… • algebraically • from their graphs • from tabular definitions.

  8. Homework • From Section 1-3: • Q1-Q10 (as quickly as possible) • 15, 17. • From Section 1-4: • Reading Analysis • Q1-Q10 • 1, 2, 5, 7, 9, 10, 12-15. • Due Friday, 9/17.

  9. To the Lab • …where you can work on the lab assignment, or the HW if already done.

  10. Clean-up / Reminders • Pick up all trash / items. • Push in chairs (at front and side tables). • See you tomorrow!

More Related