Math 118 Quiz 2

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

1. horizontal stretch/compression
2. horizontal shift
3. vertical flip
4. vertical stretch/compression
5. horizontal flip
6. 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.