'Graph shifts' diaporamas de présentation

Practice with Quick Sketches

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Graphing Cotangent

Graphing Cotangent. Objective. To graph the cotangent. 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.

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Cosecant

Cosecant. Objective. To graph the cosecant. y = csc X. Recall from the unit circle that csc ? = r/y. csc ? is undefined whenever y = 0. y = csc x is undefined at x = 0 , x = ? and x= 2 ?. Domain of Cosecant Function.

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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 ? .

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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 ? .

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y = csc X

y = csc X. Recall from the unit circle that csc ? = r/y. csc ? is undefined whenever y = 0. y = csc x is undefined at x = 0 , x = ? and x= 2 ?. Domain of Cosecant Function.

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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. The tangent function is undefined at + k ? . Asymptotes are at every multiple of + k ? .

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y = sec x

y = sec x. Recall from the unit circle that: sec = r/x. sec is undefined whenever x = 0. Between 0 and 2 ?, y = sec x is undefined at x = ? /2 and x = 3 ? /2. Domain. Since sec x is undefined at ? /2, 3 ? /2, etc., the asymptotes appear at ? /2 + k ?. Range of Secant Function.

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y = cot x

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.

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y = sec x

y = sec x. Recall from the unit circle that: sec = r/x. sec is undefined whenever x = 0. Between 0 and 2 ?, y = sec x is undefined at x = ? /2 and x = 3 ? /2. Domain. Since sec x is undefined at ? /2, 3 ? /2, etc., the asymptotes appear at ? /2 + k ?. Range of Secant Function.

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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. The tangent function is undefined at + k ? . Asymptotes are at every multiple of + k ? .

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y = cot x

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.

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Complex Numbers

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Section 1.4 Transformations and Operations on Functions

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5.3 Translating Parabolas

5.3 Translating Parabolas. SWBAT translate parabolas using vertex form. Do Now. Identify the parent function of each function. Then graph the function by translating each parent function. y = |3x| + 2 y = -|x + 1| - 1 Write an equation for each translation. 3. y = |2x|, 2 units down

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