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## PowerPoint Slideshow about ' Graphing Cotangent' - abel-abbott

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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

- 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

- This means that one complete cycle occurs between zero and .
- The period is .

Max and Min Cotangent Function

- Range is unlimited; there is no maximum.
- Range is unlimited; there is no minimum.

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 Functiony = cot x

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) +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) +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) +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 (2x + ) + 2

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