Graphing Cotangent

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Show your work for each problem.

1.
What is the period of ?
1. a)
2. b)
3. c)
4. d)
2.
Where are the vertical asymptotes of ?
1. a) for integer
2. b) for integer
3. c) for integer
4. d) for integer
3.
What is ?
4.
What is ?
5.
Does the cotangent function increase or decrease within each period?
1. a)Increases
2. b)First increases, then decreases
3. c)First decreases, then increases
4. d)Decreases
6.
What is the period of ? Express your answer as a fraction of (e.g., type 'pi/2' for ).
7.
What is the phase shift of ?
1. a)No phase shift
2. b) to the left
3. c) to the right
4. d) to the right
8.
Find the period and asymptotes of .
9.
Identify the transformations in .
10.
What is the first positive asymptote of ?
1. a)
2. b)
3. c)
4. d)
11.
For , find the period, phase shift, and the first positive asymptote.
12.
What is the range of ?
1. a)
2. b)
3. c)
4. d)
13.
If has asymptotes at , what is ?
14.
Find the equation of a cotangent function with period , phase shift right, and vertical shift up by 3.
15.
Which equation represents a cotangent function with asymptotes at ?
1. a)
2. b)
3. c)
4. d)