Y tan x
This presentation is the property of its rightful owner.
Sponsored Links
1 / 16

y = tan x PowerPoint PPT Presentation


  • 78 Views
  • Uploaded on
  • Presentation posted in: General

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  .

Download Presentation

y = tan x

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Y tan x

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

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

Period of Tangent Function

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

  • The period is .


Critical points

Critical Points

  • The range is unlimited; there is no maximum.

  • The range is unlimited; there is no minimum.


Y tan x key points

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


Graph of the parent function

Graph of the Parent Function


Parent function

Parent Function: (-,)


The graph y a tan b x c d

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 4 tan x

y = 4 tan x


Y a tan b x c d

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 tan 2x

y = tan 2x


Y a tan b x c d1

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 tan x 2

y = tan (x - /2)


Y a tan b x c d2

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.


Y tan x 3

y = tan x + 3


Y 3 tan 2 x 3

y = 3 tan (2x-) - 3


  • Login