1 / 18

Graphing Tangent

Graphing Tangent. Objective: To graph the tangent function. 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  .

jordan-huffman
Download Presentation

Graphing Tangent

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. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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. • y=tan 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| > 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.

  10. y = 4 tan x

  11. 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.

  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

More Related