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# Graphing Cotangent PowerPoint PPT Presentation

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.

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

• 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.

### 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.