Graphing Tangent

1
Graphing Tangent

• Objective
• To graph the tangent function

2
y tan x

• Recall from the unit circle
• that tan ?
• tangent is undefined when x 0.
• ytan x is undefined at x and x .

3
Domain/Range of the Tangent Function

• The tangent function is undefined at k?.
• Asymptotes are at every multiple of k ?.
• The domain is (-?, ? except k ?).
• Graphs must contain the dotted asymptote lines.
  These lines will move if the function contains a
  horizontal shift, stretch or shrink.
• The range of every tan graph is (-?,? ).

4
Period of Tangent Function

• One complete cycle occurs between and .
• The period is ?.

5
Critical Points

• The range is unlimited there is no maximum or
  minimum.

6
Parent Function y tan x Key Points

• asymptote. The graph approaches
• -? as it near this asymptote
• Key points ( , -1), (0,0), ( , 1)
• asymptote. The graph approaches
• ? as it nears this asymptote

7
Graph of the Parent Function
8
Parent Function (-?,?)
9
The Graph y a tan b (x - c) d

• a vertical stretch or shrink
• If a gt 1, there is a vertical stretch.
• If 0ltalt1, there is a vertical shrink.
• If a is negative, the graph reflects about the
• x-axis.

10
y 4 tan x
11
y a tan 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.

12
y tan 2x
13
y a tan b (x - c) d

• c horizontal shift
• If c is negative, the graph shifts left c units.
  (x - (-c)) (x c)
• If c is positive, the graph shifts right c units.
  (x - (c)) (x - c)

14
y tan (x - ?/2)
15
y a tan b (x-c) d

• d vertical shift
• If d is positive, graph shifts up d units.
• If d is negative, graph shifts down d units.

16
y tan x 3
17
To Find Asymptotes
18
y 3 tan (2x-?) - 3