y cot x

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 gt 1, there is a vertical stretch.
• If 0 lt a lt 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 gt 1, there is a horizontal shrink.
• If 0 lt b lt 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