1 / 19

Graphing Cotangent

Graphing Cotangent. Objective. To graph the cotangent. y = cot x . Recall that cot  = . cot  is undefined when y = 0. y = cot x is undefined at x = 0, x =  and x = 2 . Domain/Range of Cotangent Function.

abel-abbott
Download Presentation

Graphing Cotangent

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. Graphing Cotangent

  2. Objective • To graph the cotangent

  3. y = cot x • Recall that • cot  = . • cot  is undefined when y = 0. • y = cot x is undefined at x = 0, x =  and x = 2.

  4. Domain/Range of Cotangent Function • Since the function is undefined at every multiple of , there are asymptotes at these points. • Graphs must contain the dotted asymptote lines. These lines will move if the function contains a horizontal shift, stretch or shrink. • There are asymptotes at every multiple of . • The domain is (-,  except k) • The range of every cot graph is (-, ).

  5. Period of the Function • This means that one complete cycle occurs between zero and . • The period is .

  6. Max and Min Cotangent Function • Range is unlimited; there is no maximum. • Range is unlimited; there is no minimum.

  7. Parent Function Key Points • x = 0: asymptote. The graph approaches  as it approaches this asymptote. • x = : asymptote. The graph approaches - as it approaches this asymptote.

  8. Graph of Parent Functiony = cot x

  9. The Graph: y = a cot b(x-c) +d • a = vertical stretch or shrink • If |a| > 1, there is a vertical stretch. • If 0 < |a| < 1, there is a vertical shrink. • If a is negative, the graph reflects about the x-axis.

  10. y = 4 cot x

  11. The Graph: y = a cot b(x-c) +d • b= horizontal stretch or shrink. • Period = . • If |b| > 1, there is a horizontal shrink. • If 0 < |b| < 1, there is a horizontal stretch.

  12. y = cot 2x

  13. The Graph: y = a cot b(x-c) +d • c = horizontal shift. • If c is negative, the graph shifts left c units. • If c is positive, the graph shifts right c units.

  14. y = cot (x - )

  15. The Graph: y = a cot b(x-c) +d • d= vertical shift. • If d is positive, the graph shifts up d units. • If d is negative, the graph shifts down d units.

  16. y = cot x - 4

  17. To find the asymptotes

  18. y = cot (2x + ) + 2

  19. y = - 2cot ( ½ x - ) - 3

More Related