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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. Since the function is undefined at every multiple of  , there are asymptotes at these points.

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y = cot x

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

  2. 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 (-, ).

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

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

  5. Parent Function Key Points • x = 0: asymptote. The graph approaches  as it approaches this asymptote. • ( , 1) , ( , 0) , ( , -1) • x = : asymptote. The graph approaches - as it approaches this asymptote.

  6. Graph of Parent Functiony = cot x

  7. 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.

  8. y = 4 cot x

  9. 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.

  10. y = cot 2x

  11. 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.

  12. y = cot (x - )

  13. 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.

  14. y = cot x - 4

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

  16. y = - 2cot ( ½ x - ) - 3

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