1 / 22

Math 2: Unit 5B Day 3

Math 2: Unit 5B Day 3. How do we solve problems using piecewise functions, step functions, and greatest integer functions?. Today’s Brainteaser Can you figure out the word/phrase represented by the puzzle?. Gone. Polygon. Square Roots. 2. Piecewise Functions.

senta
Télécharger la présentation

Math 2: Unit 5B Day 3

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. Math 2: Unit 5BDay 3 How do we solve problems using piecewise functions, step functions, and greatest integer functions?

  2. Today’s Brainteaser Can you figure out the word/phrase represented by the puzzle? Gone Polygon Square Roots 2

  3. Piecewise Functions • A piecewise function is a function represented by more than a single equation. The domain indicates when to use each equation.

  4. Evaluate the function: To evaluate a piecewise function, look at the domain!

  5. Evaluate the function:

  6. Points of discontinuity • X-values where there are gaps in the graph • Ex: *because there is a gap in the graph at x = 1, this is a point of discontinuity.

  7. Graphing Piecewise Functions Domain: Range: Intercepts: Points of discontinuity:

  8. Graphing Piecewise Functions Domain: Range: Intercepts: Points of discontinuity:

  9. Graphing Piecewise Functions Domain: Range: Intercepts: Points of discontinuity:

  10. Graphing Piecewise Functions Domain: Range: Intercepts: Points of discontinuity:

  11. Writing an absolute value function as a piecewise function • Graph the absolute value function • Find linear equations that represent each piece of the graph • Create a domain restriction based on the vertex • Write the function as a piecewise function

  12. Writing an absolute value function as a piecewise function Vertex: Open up or down? Left side of vertex: Right side of vertex:

  13. Writing an absolute value function as a piecewise function Vertex: Open up or down? Left side of vertex: Right side of vertex:

  14. Writing an absolute value function as a piecewise function Vertex: Open up or down? Left side of vertex: Right side of vertex: GA Notetaking Guide Page 52 – 53 # 1 – 7 all, #12 – 14 all

  15. Step Function • A piecewise function that is defined by a constant value over each part of its domain. • Its graph resembles a set of stairs

  16. Graph the following step functions

  17. Graph the following step functions

  18. Greatest integer function: y = [x] The greatest integer function, y = [x] is defined as follows: [x] is the greatest integer that is less than or equal to x.

  19. Reflection of the greatest integer function

  20. Graph using transformations y=[x+3] y = [x-1]

  21. Graph using transformations y=[x]+2 y = [x-2]+1

  22. Real world applications of step functions • In 2005 the cost C (in dollars) to send US postal service express mail up to 3 pounds depended on the weight w (in ounces) according to the function below. What is the cost to send a package weighing: • 13 ounces? • 3 ounces? • 20 ounces? • 5 ounces? REMEMBER: Test is ___________!!!! Do the REVIEW!!! HW: Page 52 (# 5 – 11) and Page 53 (# 5 – 10, 23 – 26)

More Related