Transformations General
The A in y=asin(b(x-h))+k affects the __________ of the graph.
Amplitude
The period of y=sin(x) and y=cos(x) is ________.
2pi
The zeros of y=sin(x) produce _________ for y=csc(x).
Vertical asymptotes
The amplitude of y=2cos(3x) is _____.
2
The vertical stretch/compression of y=cot(x-3) is ______.
1
The b in y=asin(b(x-h))+k affects the ______________ of the graph.
Period
The domain of both y=sin(x) and y=cos(x) is ____________.
All Real Numbers
The vertical asymptotes of y=sec(x) are in the same place as the ___________ of y=cos(x) .
Zeros
The period of y=2sin(4x) is ________.
pi/2
The stretch/compression of y=-2csc(x)
2
The h in y=asin(b(x-h))+k affects the ___________ of the graph.
Phase shift
The range of both y=sin(x) and y=cos(x) is _________.
[-1,1]
The range of both y=tan(x) and y=cot(x) are ____________.
All Real Numbers
The maximum value of
y=1/3sin(5x)
1/3
The period of
y=2tan(3x)
pi/3
The general equation for the period of sin, cos, csc, and sec is _______________.
P=(2pi)/b
The beginning of one period of the graph
y=sin(x)
is at the:
a) maximum
b) midline
c) minimum
b) midline
The range of y=sec(x) is ____________.
(-inf, -1] U [1, inf)
The minimum value of
y=3sin(x)+1
-2
The phase shift of
y=sec(x-pi/2)+5
Right pi/2
The general equation for the period of tan and cot is ____________.
P=pi/b
The beginning of the cycle of y=cos(x) starts at the maximum value. It will start at the minimum value if you change the equation by ______________.
Multiplying a negative out front
The domain of y=tan(x) is ____________.
All real numbers except where cos(x)=0
The phase shift of
y=-3sin(2x+6)+1
The vertical shift of
y=2cot(x+pi)-4
Down 4