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Area of a circle
A=πr²
Area of a rectangle
A=lw
Area of a triangle
A=1/2bh
Volume of a cylinder
V=πr²h
Volume of a rectangular solid
V=lwh
Volume of a triangular prism
V=(1/2bh)h
Circumference of a circle
C=2πr
Even symmetry: if _, then _
if (a,b), then (-a, b)
Odd symmetry: If _, then _
if (a,b), then (-a,-b)
Symmetric about the line y=x: If _, then _
If (a,b), then (b,a)
What are the domain restrictions for a log function?
x > 0
List the asymptotes for y=2^x
horizontal
General equation for a vertical shift
f(x) + c
How do you demonstrate a vertical shift on a set of points?
Either add or subtract c from the y-values
General equation for a vertical stretch/compression
cf(x)
When is cf(x) a vertical stretch?
when c is greater than one
When is cf(x) a vertical compression?
when c is greater than zero, but less than one
How do you demonstrate a vertical stretch on a set of points?
multiply y values by c
How do you demonstrate a vertical compression on a set of points?
divide y values by c
General equation for horizontal shift
f(x+c)
How do you demonstrate a horizontal shift on a set of points?
Either add or subtract c from the x-values
If c is positive during a horizontal shift, do you add or subtract c from the x-values?
subtract
If c is negative during a horizontal shift, do you add or subtract c from the x-values?
add
General equation for a horizontal compression/stretch
f(cx)
When is f(cx) a compression?
when c is greater than one
When is f(cx) a stretch?
when c is greater than one but less than zero
How do you demonstrate a horizontal stretch on a set of points?
multiply x-values by the reciprocal of c
How do you demonstrate a horizontal compression on a set of points?
divide x-values by c
What is -f(x)?
vertical flip, reflection about the x-axis
How do the points of a function change when there is a vertical flip/reflection about the x-axis?
x remains unchanged, y switches signs
What is f(-x)?
horizontal flip, reflection about the y-axis
How do the points of a function change when there is horizontal flip/reflection about the y-axis?
x switches signs, y remains unchanged
What must you do if you have a horizontal shift and another horizontal transformation?
factor the argument to see the true shift
Steps for a sequence of transformation
horizontal stretch/compression
horizontal shift
vertical flip
vertical stretch/compression
horizontal flip
vertical shift
Recursive model equation
Ysubt = (1+n)Ysub(t-1)
what is n?
the number of iterations
Explicit function equation
Ysubt = (1+n)^t*ysubzero,
what can n be thought of as?
the independent variable
what can y be thought of as?
the dependent variable
when should you use recursive models?
discrete (not continuous)
when should you use explicit function?
with continuous
What should you do if an explicit function is used for a discrete-valued function?
restrict the domain
define variable for y=ab^x
y=0 is the horizontal asymptote, a is the initial amount, b is the growth factor, and x is the number of growth periods
describe b = 1 +r
the growth factor equals the growth rate plus one
what is asubn?
the future value of an initial deposit
compounding recursive formula?
Asubt=asub(t-1)*(1+r/n)
compounding explicit formula?
A=Asubzero*e^rt
e=_____?
(1+I/n)^n
What happens when interest is compounded more than once a year?
annual interest rate is divided by the number of compounding periods
(x^a)^b = _____?
x^a*b
Exponential graphs will contain what?
(0,1) (1,b) (-1, 1/b) and y=0
b^m+n=_____?
b^m+b^n
Exponential functions with a base between 0 and 1, or a negative coefficient model _____?
exponential decay
(a*b)^n =______?
a^n*a^b
(a^p)^q=______?
a^pq
a^-p
1/a^p
domain and range of y=b^x
domain: all real numbers, range y>0
horizontal stretches of compression can be modeled as ____?
a change of base
a horizontal shift can be modeled as?
a vertical stretch or compression
What is the annual percentage yield?
effective annual rate of return taking into account the effect of compounding interest.
Note
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