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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.

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Graphing Cotangent

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  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

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