1 / 17

Sullivan Algebra & Trigonometry: Section 3.5 Graphing Techniques: Transformations

Sullivan Algebra & Trigonometry: Section 3.5 Graphing Techniques: Transformations. Objectives Graph Functions Using Horizontal and Vertical Shifts Graph Functions Using Compressions and Stretches Graph Functions Using Reflections about the x-Axis and y-Axis.

Download Presentation

Sullivan Algebra & Trigonometry: Section 3.5 Graphing Techniques: Transformations

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. Sullivan Algebra & Trigonometry: Section 3.5Graphing Techniques: Transformations • Objectives • Graph Functions Using Horizontal and Vertical Shifts • Graph Functions Using Compressions and Stretches • Graph Functions Using Reflections about the x-Axis and y-Axis

  2. Example: Use the graph of to obtain the graph of First, find points on the graph of f and g.

  3. (2, 6) (1, 3) (2, 4) (0, 2) (1, 1) If a real number c is added to the right side of a function y = f(x), the graph of the new function y = f(x) + c is the graph of fshifted vertically up (for c> 0).

  4. Example: Use the graph of to obtain the graph of First, find points on the graph of f and g.

  5. (2, 4) (1, 1) (2, 1) (1, -2) (0, -3) If a real number c is subtracted from the right side of a function y = f(x), the graph of the new function y = f(x) - c is the graph of fshifted vertically down (for c> 0).

  6. Example: Use the graph of to obtain the graph of First, find points on the graph of f and g.

  7. (0, 4) (2, 4) (-1, 1) (-3, 1) (1, 1) (-2, 0) If a real number c is subtracted from the argument x of a function y = f(x), the graph of the new function y = f(x - c) is the graph of fshifted horizontally right (if c > 0) or left (if c < 0).

  8. (-1, 4) (2, 4) (0, 0) (-3, 0) (-1, 2) (-3, -2) Example: Graph the function

  9. Example: Use the graph of to obtain the graph of First, find points on the graph of f and g.

  10. (2, 4) (1, 2) (2, 2) (1, 1) When the right side of a function y = f(x) is multiplied by a positive number k, the graph of the new function y = kf (x) is a vertically compressed (if 0 < k < 1) vertically stretched (if k > 1) version of the graph of y = f(x).

  11. Example: Graph each of the following functions: Y2 Y1 Y3 When the argument of a function y = f (x) is multiplied by a positive number k, the graph of the new function y = f(kx) is a horizontally stretched (if 0 < k < 1) or horizontally compressed (if k > 1) version of the graph of y = f (x).

  12. (4, 2) (4, 6) (8, 6) Example: Graph

  13. Example: Use the graph of to obtain the graph of First, find points on the graph of f and g.

  14. (-3, 9) (2, 4) (2, -4) (-3, -9) When the right side of a function y = f(x) is multiplied by -1, the graph of the new function y = -f (x) is the reflection about the x-axis of the graph of the function y = f(x).

  15. Example: Use the graph of to obtain the graph of First, find points on the graph of f and g.

  16. (9, 3) (-9, 3) (-4, 2) (4, 2) (-1, 1) (1, 1) When the argument of a function y = f (x) is multiplied by -1, the graph of the new function y = f(-x) is the reflection about the y-axis of the graph of y = f (x).

  17. (-4,2) (4,2) (-1,1) (1,1) (-1,-1) (-4,-2) Example: Graph

More Related