Download presentation

Presentation is loading. Please wait.

Published byAbbey Gorman Modified over 2 years ago

1
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 =.

2
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 (- , ).

3
Period of Tangent Function This also means that one complete cycle occurs between and. The period is .

4
Critical Points The range is unlimited; there is no maximum. The range is unlimited; there is no minimum.

5
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

6
Graph of the Parent Function

7
Parent Function: (- , )

8
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.

9
y = 4 tan x

10
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.

11
y = tan 2x

12
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)

13
y = tan (x - /2)

14
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.

15
y = tan x + 3

16
y = 3 tan ( 2 x- ) - 3

Similar presentations

OK

Notes Over 9.2 Graphing a Rational Function The graph of a has the following characteristics. Horizontal asymptotes: center: Then plot 2 points to the.

Notes Over 9.2 Graphing a Rational Function The graph of a has the following characteristics. Horizontal asymptotes: center: Then plot 2 points to the.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on history of earth Ppt on amplitude shift keying modulation Convert word doc to ppt online student Ppt on gujarati culture family Ppt on work and energy class 11 Field emission display ppt online Ppt on image compression using matlab Ppt on porter's five forces analysis of amazon Just in time ppt on production Ppt on idiopathic thrombocytopenia purpura therapy