day 2 combined sorta

Relation

Set of ordered pair

rule that relates values from domain to range

ordered pair

pair of objects taken in specific order

Set

collection of well-defined & distinct objects called elements that share a common characteristic

Set is represented by

{brackets}

Domain

set of all x values, input

Range

set of all y values, output

Function

special relation

every x value/input is associated with one value of the y value/output

When is something not a function?

1 input has more than one output

Input-output relation

one quantity depends on the other quantity

Input Quantity

Domain

Output Quantity

Range

Every input …

must have at least one output

2 different inputs …

can have the same output

Different ways to present a function

Notation, Tabular, Mapping, Sets, Graph

Notation

used to express y as function of x

Y (Notation)

dependent variable/output/range

X (notation)

independent variable/input/domain

f(x) (Notation)

rule/condition

How to solve for tabular

substitute

types of correspondents

one to one, many to one, one to many

Mapping

show how elements are paired

“flow chart’

show input/output of values

Correspondent/s that are considered a function

one to one & many to one

Correspondent/s that are not considered a function

one to many

Sets

AKA Roster Notation

How to ideintify if function in sets

no x value repeated

How to identify if function in graphing

vertical/imaginary line test

Linear Function formula

f(x) = mx + b

m & b are real number, not equal to zero

If Linear Function is zero what does it become?

Undefined. Therefore you can’t graph it.

y & f(x)

interchangeable

Function IRL

Biology, Chemistry, Economics, Statistics, Engineering

Function in Biology

plant growth rate as function of sun & water

animal’s growth rate

Function in Computer

machine speed as function of memory/battery rate/temperature

Function in Social Science

divorce rate (function of race, age, income()

function in economics

inflation as function of oil/unemployment

salary = hours working

height of students

canned good price = no. bought

simplifying algebraic expression

like terms can be simplified by adding/subtracting coefficients

2 monomials

add/subtract only like terms

adding monomial

add coefficient, keep variables & exponent

addition of function

let f & g be a function

sum (f+g)(x)

function defined (f+g)(x)=f(x)+g(x)

subtraction of function

let f & g be a function

difference (f-g)(x)

function defined (f-g)(x)=f(x)-g(x)

multiplication of function

(f.g)=f(x).g(x)

division of function

(f/g)(x) = f(x)/g(x)

The earth’s body fromed from

spinning solar nebula (sun)

how did spinning solar nebula develop

developed depending on proximity from sun & interaction w/ floating nearby masses

earth’s shape

oblate spheroid

due to gravity & rotation

Gravity pulls mass closer to what

gravity pulls mass closer to center of it’s core. earth’s core is the center of gravity

how does planet form sphere like shape

planet contracts

sphere is distorted by

centrifigual force

angular momentum is maximum @

equator (bulging outward)

isaac newton predicted

a similar shape to that of oblate spheroid (by observign earth’s rotation)

geodesy

study of earth’s shape

importance of geodesy

satellites orbit, navigationt ool, improve global positioning satellites (GPS)

Age of the Earth is

1/3 age of universe

4 billion years old

earth flung out of

solar nebula & started out as an immensely hot gaseous mass

earth’s formative state

constantly bombarded by meteorite/comets/planetary bodies

most parts of the earth were ____ causing _____

molten

collision w/ other planetary activities (causiing volcanic activity)

Caused planet tilt

large collision

volcanoes were ___ , ___ , ___& contributed to ____

constantly erupting/flying planetary debris/spinning

earth’s present shape

where did water come from?

space. since earth had no protectice layer back then

Which collected water & what did they do?

lower elevations/low-lying surfaces. form ocean basins

outgassing of volcanoes formed what

promordial atmosphere (no oxygen & toxic gases)

formation of 1st inhabitant

oxygen

evolution of earth prompted

production of other materials vital to life

Geosphere is the layer that incldues

interior structure, rocks, minerals, landforms, physical processes that shape Earth’s surface

Continents and ocean floor

parts of the geosphere

Scientists that study Geosphere

Geologists

geosphere covers

solid ground (surface to deep core)

lithosphere only covers

the crust

three main layers of earth’s internal structure

crust, mantle, core

unique features

why do you only see surface of crust?

this is the part of the earth where we live

Different layers of the earth vary in

density, mineral composition, temperature, thickness

they have allowed the identification of materials in Earth’s interior through seismic waves

modern technology

2 types of waves traveling thru earth

p & s waves

P wave

travel fast through solids & liquids

particle motion: horizontal

S wave

travel slower than p waves. only thru solid

partical motion: vertical

they incessantly study the components of earth through sesimic waves

seismologists & volcanologsits

The crust consists of a ___ to ____ km thick layer of _____ & ___ continental crust

5, 70

oceanic, continental

Which is thicker: Continental or oceanic?

continental

8 elements that comprise the crust

O, Si, Al, Fe, Ca, Na, K, Mg

(Oxygen, Silicon, Aluminum, Iron, Calcium, Sodium, Potassium, Magnesium)

We use the elements of the crust to produce things such as

Glass (SiO2) & concrete (CaCO3) & steel

where is the mohorovicic discontinuity situated?

between crust and mantle

mohorovicic discontinuity is AKA

Moho

Who discovered mohorovicic discontinuity?

croatian seismologist

andrija mohorov

1909

Why is is it called discontinuity (mohorovicic)

velocity of seismic waves behave dif. as they travel through this layer before reaching mantle

moho is now recognized as

transition boundary dividing crust from mantle

extra sublayer of mantle

asthenosphere

where does the asthenosphere lie?

upper part of mantle, directly below crust

The extreme _____ & ___ in the asthenosphere cause rock to become _____ & move like ______

temperature, pressure

ductile

liquid

what causes asthenosphere to break?

flow of semi molten rocks in some aread of crust

the rigid parts of crust

float/move slowly on liquid, supporting movement of plates (plate tectonic theory)

mantle is made of

silicate rocks

mantle is considered as ____ layer of the earth

thickest

mantle holds how much of earth’s volume

84%

most of the mantle is ____, but behaves like _____

solid

viscous fluid

the limited time knowledge that scientists have on mantle is derived from

xenoliths

where do xenoliths come from?

embedded/trapped in rocks that come from a volcano

the rocks trapped in magma contain what?

most of the primary rocks that originated from earth’s interior

volcanologists collect samples from ____ ?

rocks coming from volcanism

spreading mid-oceanic ridge

the gutenberg discontinuity serves as a _____ boundary between the _____ & _______

transitional

lower mantle & outer core

who discovered gutenberg discontinuity

beno gutenberg

why is the gutenberg discontinuity not constant?

changes in heat flow