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y = cot x . Recall that cot ï‘ = . cot ï‘ is undefined when y = 0. y = cot x is undefined at x = 0, x = ï° and x = 2 ï°. Domain/Range of Cotangent Function. Since the function is undefined at every multiple of ï° , there are asymptotes at these points.
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y = cot x • Recall that • cot = . • cot is undefined when y = 0. • y = cot x is undefined at x = 0, x = and x = 2.
Domain/Range of Cotangent Function • Since the function is undefined at every multiple of , there are asymptotes at these points. • Graphs must contain the dotted asymptote lines. These lines will move if the function contains a horizontal shift, stretch or shrink. • There are asymptotes at every multiple of . • The domain is (-, except k) • The range of every cot graph is (-, ).
Period of the Function • This means that one complete cycle occurs between zero and . • The period is .
Max and Min Cotangent Function • Range is unlimited; there is no maximum. • Range is unlimited; there is no minimum.
Parent Function Key Points • x = 0: asymptote. The graph approaches as it approaches this asymptote. • ( , 1) , ( , 0) , ( , -1) • x = : asymptote. The graph approaches - as it approaches this asymptote.
The Graph: y = a cot 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.
The Graph: y = a cot 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.
The Graph: y = a cot b(x-c) +d • c = horizontal shift. • If c is negative, the graph shifts left c units. • If c is positive, the graph shifts right c units.
The Graph: y = a cot b(x-c) +d • d= vertical shift. • If d is positive, the graph shifts up d units. • If d is negative, the graph shifts down d units.
