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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Graphing Cotangent

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Graphing cotangent

Graphing Cotangent


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.


Graph of parent function y cot x

Graph of Parent Functiony = cot x


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.


Y 4 cot x

y = 4 cot x


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.


Y cot 2x

y = cot 2x


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.


Y cot x1

y = cot (x - )


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 x 4

y = cot x - 4


To find the asymptotes

To find the asymptotes


Y cot 2 x 2

y = cot (2x + ) + 2


Y 2cot x 3

y = - 2cot ( ½ x - ) - 3


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