1 / 17

Understanding Graph Transformations: An Introduction to Vertex and Parent Functions

This guide focuses on translating graphs, which involves shifting them up, down, left, or right. By understanding the general transformation equations, we can describe the location of a graph through its vertices. The key points include identifying parent functions, understanding vertical and horizontal shifts, and recognizing the significance of the vertex in determining graph transformations. We provide examples and practice problems to reinforce learning. By the end, you will know how to identify vertices and write equations that represent the shifted graphs.

overton
Télécharger la présentation

Understanding Graph Transformations: An Introduction to Vertex and Parent 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. Warm up Find: g(1) and g(5) + 7 Don’t freak out! Just plug the number in for x and solve.

  2. Translating graphs Part 18.2a (skipped 8.1)

  3. What does this mean? • Simply picking up a graph, and moving it. Either up and down, or side to side.

  4. What these can look like… • Same graph, just in a new location

  5. We need a way to explain the location of a graph using equations.

  6. First we need to know the general equation for each function. They are called the Parent Functions

  7. The main three you will work with for now

  8. What is a vertex? • The peak in the curve, or the tip of the graph. • We will use the vertex to figure out where the graph moved.

  9. What is the coordinates for the vertex of the blue graph? • (0,0) • Of the red? • (-3, .5)

  10. What is the coordinates for the vertex of the blue graph? • (0,0) • Of the red? • (3, 0)

  11. Looking at the vertex is the easiest way to tell where the function shifted.

  12. General Transformation Equation • k=vertical shift (up and down) • +k is up • -k is down. • h=horizontal shift (side to side) • (x-h) is shifted to the RIGHT • (x+h) is shifted to the LEFT

  13. Example 1: (blue is original, red is shifted) • Questions to ask yourself • What is the parent function? y=x 2. Has it shifted left or right? No 3. Has it shifted up/down? Yes, it went up 3. 4. What is the equation?

  14. Example 2: blue is original, red is shifted

  15. Example 3

  16. You try! Blue is original. • Answer:

  17. Homework • Problems 1 and 2 • For 2, identify the vertices AND write an equation for each graph.

More Related