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68 Cards in this Set
- Front
- Back
domain:
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all possible x inputs
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domain 1/x
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x cannot =0
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domain √x and all other even roots
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x must be greater than or equal to 0
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domain tan x
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x cannot be any
odd number pi / 2 (pi/2, 3pi/2, -pi/2) |
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domain logx
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x>0 (x cannot be less than OR equal to 0)
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inverse fxn definition
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y=f(x) then x=f^-1(y)
**f(x) must satisfy HLT, so its inverse satisfies VLT |
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domain/range of inverse functions
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domain of f(x) is range of its inverse, range of f(x) is domain of its inverse
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how to get a function's inverse when one does not exist
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restrict the domain to allow HLT to pass
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what to restrict y=sinx domain to to allow for sin^-1(x)
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restrict from -pi/2 to pi/2
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what to restict y=cosx domain to, to allow for cos^-1(x)
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0 to pi
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π/6
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30 degrees
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sin0
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0
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cos0
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1
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tan 0
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0
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sin π/6
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1/2
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cos π/6
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√3/2
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tan π/6
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1/√3
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sin π/4
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1/√2
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cos π/4
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1/√2
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tan π/4
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1
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sin π/3
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√3/2
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cos π/3
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1/2
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tan π/3
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√3
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sin π/2
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1
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cos π/2
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0
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tan π/2
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DNE
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(sinx)^2
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1- (cosx)^2
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(cosx)^2
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1-(sinx)2
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(secx)^2
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1+(tanx)^2
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(cscx)^2
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1+(cotx)^2
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pythagorean ID's : 1=
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(sinx)^2+(cosx)^2
(secx)^2-(tanx)^2 (cscx)^2-(cotx)^2 |
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odd function
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f(x)=-f(x)
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even function
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f(x)=f(-x)
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sin: odd or even function
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sin=ODD
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cos: odd or even function
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EVEN
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sin2x
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2sinxcosx
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(sinx)^2
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1/2(1-cos2x)
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(cosx)^2
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1/2(1+cos2x)
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sin(x+y)
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sin(y) * cos(x)+ sin(x)* cos(y)
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cos(x+y)
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cos(x)*cos(y)-sin(x)*sin(y)
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sinx: domain and range
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domain: all real numbers
range: [-1,1] |
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cosx: domain and range
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domain: all real numbers
range: [-1,1] |
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tanx: domain and range
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domain: x cannot equal any
odd π/ 2 range: all real numbers |
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sin^-1 (1/2)
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π/6
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graph of y= e^x
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logx graph
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log x =n
b |
b^n=x
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log(ac)
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log a + log c
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log b
b |
1
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log a^c
b |
c*loga
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log (x)^b
b |
logx/logb
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log 1
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0
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to find the domain and range of a composite function f(g(x))
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1) x must be in domain of g
2) g(x) must be in domain of f |
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f(x) +c
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shift up c
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f(x+c)
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shift left c
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f(x-c)
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shift right by c
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f(x)-c
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shift down c
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c*f(x)
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vertical stretch by c times
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f(cx)
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horiztonal shrink by c times
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f(c/x)
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vertical stretch
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sin2x
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period shrinks by 2: so the period becomes π
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-f(x)
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reflect about the y axis
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f(-x)
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reflect about the x axis
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what does the slope of a tangent line indicate
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INSTANTANEOUS rate of change
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limit as x approaches 0+
1/sinx |
DNE (oscillates infinitely quickly at x=0)
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lim x-> + infinity tan^-1(x)
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π/2
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lim x->- infinity of 1/x
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0
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lim x-> - infinity sinx
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DNE (oscillates)
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