1 / 13

2.2 – Translate Graphs of polynomial functions

2.2 – Translate Graphs of polynomial functions. Coach Bianco. Unit 2.2 – Evaluate and Graph Polynomial Functions. Georgia Performance Standards: MM3A1a – Graph simple polynomial functions as translations of the function f(x) = ax n .

alyson
Download Presentation

2.2 – Translate Graphs of polynomial functions

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. 2.2 – Translate Graphs of polynomial functions Coach Bianco

  2. Unit 2.2 – Evaluate and Graph Polynomial Functions • Georgia Performance Standards: • MM3A1a – Graph simple polynomial functions as translations of the function f(x) = axn. • MM3A1c – Determine whether a polynomial function has symmetry and whether it is even, odd, or neither • MM3A1d – Investigate and explain characteristics of polynomial functions, including domain and range, intercepts, zeros, relative and absolute extrema, intervals of increase and decrease, and end behavior.

  3. Unit 2.2 – Evaluate and Graph Polynomial Functions • Translate a polynomial function vertically • Translate a polynomial function horizontally • Translate a polynomial function

  4. What does it mean to translate? • Metaphrase • Paraphrase • Rendering • Rendition • Rephrasing • Restatement • Adaptation • Construction • Decoding • Elucidation • Explanation • Key

  5. What are we actually doing? • Comparing two things to each other (In our case, functions) • This is something you’ve actually done before!

  6. Comparing Functions… What are we looking for? Check list: Vertical shift up or down? Horizontal shift left or right? Domain & Range Symmetric? x & y intercepts End behavior • You have to always graph both functions to compare them! • Write down everything you can think of! • How do we compare two functions? • Make a table (I suggest -2,-1,0,1,2 for your input) • Connect the dots!! (Make them into a curve) • Check out your end behavior (Degree & L.C.  what do they mean?)

  7. Yes, we’re using this again… • End Behavior Rules! • The end behavior of a polynomial function’s graph is the behavior of the graph as x approaches positive ∞ or negative ∞ • Degree is odd & leading coefficient positive f(x)  ∞ as x  ∞ and f(x)  -∞ as x  -∞ • Degree is odd & leading coefficient negative f(x)  -∞ as x  ∞ and f(x)  ∞ as x  -∞ • Degree is even & leading coefficient positive f(x)  ∞ as x  ∞ and f(x)  ∞ as x - ∞ • Degree is even & leading coefficient negative f(x)  -∞ as x  ∞ and f(x)  - ∞ as x -∞

  8. Example 1 • Graph g(x) = x4 + 5. Compare the graph with the graph of f(x) = x4. What do we know?

  9. Example 2 • Graph g(x) = x4 - 2. Compare the graph with the graph of f(x) = x4. What do we know?

  10. What do we notice? • Is there anything happening to the functions that are • making them shift left or right? • What about up or down?

  11. Example 3 • Graph g(x) = 2(x - 2)3 . Compare the graph with the graph of f(x) = 2x3. What do we know?

  12. Example 4 • Graph g(x) = -(x + 1)4 -3. Compare the graph with the graph of f(x) = x4. What do we know?

More Related