Graphing the Tangent Function

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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 does the first positive asymptote of occur?
1. a)
2. b)
3. c)
4. d)
3.
What is ?
4.
What is the range of ?
1. a)
2. b)
3. c)
4. d)
5.
What is ?
6.
What is the period of ? Give your answer as a fraction of (e.g., enter 'pi/2' for ).
7.
Which transformation does the '3' represent in ?
1. a)Vertical stretch by factor of 3
2. b)Vertical shift up by 3
3. c)Horizontal compression by factor of 3
4. d)Period change to
8.
Find the period and the first positive asymptote of .
9.
What happens to the asymptotes when we graph ?
1. a)They shift right by
2. b)They don't change position
3. c)They shift down by
4. d)They shift left by
10.
Find where equals 1 for in .
11.
What is the period of ? Give your answer as a multiple of (e.g., '2pi' for ).
12.
Graph . Describe how it differs from .
13.
For , what is the equation of the midline?
1. a)
2. b)There is no midline
3. c)
4. d)
14.
Find the asymptotes of in the interval .
15.
Which statement is TRUE about the graph of ?
1. a)It has a maximum value of 1
2. b)It is an odd function:
3. c)It is continuous for all real numbers
4. d)It is an even function: