1 / 15

Function Transformations

Function Transformations. Goal(s): Analyze the effects on a graph when the parameters of the equation are changed Vertical shifts Horizontal shifts Reflections Vertical stretches or compressions Horizontal stretches or compressions. Vertical Shifts. Given a graph f(x):.

cnitz
Télécharger la présentation

Function 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. Function Transformations Goal(s): Analyze the effects on a graph when the parameters of the equation are changed Vertical shifts Horizontal shifts Reflections Vertical stretches or compressions Horizontal stretches or compressions

  2. Vertical Shifts Given a graph f(x): Compare it to f(x) + 3:

  3. Vertical Shifts Given a graph f(x): Compare it to f(x) – 2:

  4. Vertical Shifts In general, a graph f(x) + k is the graph of f(x) shifted up(+) or down(-) k units. So f(x) + 5is shifted up 5 units from f(x) and f(x) – 8is shifted down 8 units from f(x).

  5. Horizontal Shifts Given a graph f(x): Compare it to f(x + 3):

  6. Horizontal Shifts Given a graph f(x): Compare it to f(x – 1):

  7. Horizontal Shifts In general, a graph f(x - h) is the graph of f(x) shifted left(+) or right(-) h units. So f(x + 5)is shifted left 5 units from f(x) and f(x – 8)is shifted right 8 units from f(x).

  8. Reflection over the x-axis Given a graph f(x): Compare it to -f(x): In general, a graph -f(x) is the graph of f(x) reflected over the x-axis.

  9. Vertical Stretch or Compression Given a graph f(x): Compare it to 2f(x):

  10. Vertical Stretch or Compression Given a graph f(x): Compare it to f(x):

  11. Vertical Stretch or Compression In general, a graph af(x) is the graph of f(x) vertically stretched or compressed. If a<1, there is a compression If a >1, there is a stretch So f(x)is vertically compressed by a factor of ½ and 4f(x)is vertically stretched by a factor of 4

  12. Horizontal Stretch or Compression Given a graph f(x): Compare it to f(3x):

  13. Horizontal Stretch or Compression Given a graph f(x): Compare it to f(x):

  14. Horizontal Stretch or Compression In general, a graph f(bx) is the graph of f(x) horizontally stretched or compressed. If b<1, there is a stretch If b >1, there is a compression So f(x)is horizontally stretched by a factor of 2 and f(4x)is horizontally compressed by a factor of

  15. Function Transformations • Given a function, f(x) the following are general transformations of the graph of the function: -af(b(x-h))+k • h  horizontal shift (left or right) • b  horizontal stretch or compression • a  vertical stretch or compression • (in front of function)  reflection over x-axis • k  vertical shift (up or down)

More Related