Presentation on theme: "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 =."— Presentation transcript:
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
Graph of the Parent Function
Parent Function: (- , )
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 = 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 = 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 = 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.