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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.
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