# y = tan x - PowerPoint PPT Presentation

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y = tan x. Recall from the unit circle: that tan  = tangent is undefined when x = 0. y=tan x is undefined at x = and x =. Domain/Range of the Tangent Function. The tangent function is undefined at + k  . Asymptotes are at every multiple of + k  .

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y = tan x

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### y = tan x

• Recall from the unit circle:

• that tan  =

• tangent is undefined when x = 0.

• y=tan x is undefined at x = and x = .

### 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 (-, ).

### Period of Tangent Function

• This also means that one complete cycle occurs between and .

• The period is .

### Critical Points

• The range is unlimited; there is no maximum.

• The range is unlimited; there is no minimum.

### y = tan x Key Points

• : asymptote. The graph approaches

- as it near this asymptote

• ( , -1), (0,0), (, 1)

• : asymptote. The graph approaches

 as it nears this asymptote

### The Graph: y = a tan 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.

### y = a tan 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.

• If b<0, the graph reflects about the y-axis.

### 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)

### 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.