Graphing cotangent
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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.

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Presentation Transcript

Objective
Objective

  • To graph the cotangent


Y cot x
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
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 (-, ).


Period of the function
Period of the Function

  • This means that one complete cycle occurs between zero and .

  • The period is .


Max and min cotangent function
Max and Min Cotangent Function

  • Range is unlimited; there is no maximum.

  • Range is unlimited; there is no minimum.


Parent function key points
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.



The graph y a cot b x c d
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.



The graph y a cot b x c d1
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.



The graph y a cot b x c d2
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.



The graph y a cot b x c d3
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.




Y cot 2 x 2
y = cot (2x + ) + 2



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