math your concept

8/3/2019 Math Your Concept

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By: Jhobel Laurente

IV CygnusSY 2011- 2012


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Relations andFunctions


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RelationFunctionRangeDomainTableArrow diagramAbscissaOrdinate


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Relation - are a set of ordered pairs.Function a rule of correspondence between twononempty sets, such that to each element of the firstset, there corresponds one and only one element of thesecond set/ is a relation which element of the domainis paired with exactly one element of the range.

Arrow Diagram : (showing the following types of relation)One to many RelationMany to one Relation

One to one RelationDomain - all possible values of x (independentvariable)Range all possible values of y (dependent variable)


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Abscissa horizontal x Ordinate Vertical y The domain (x) is not repeated All functions are relations, but not all relations

are functions.

To evaluate for f(x) at a particular value of (x)in the domain of (f), substitute the value of x toall xs in the equation of the function.

Piecewise Function a function that is dividedinto pieces.

f[f (x)] = f [f(x)] *The function of its inverse isthe inverse of its function.


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Relation involves the association or connectionof an object to another object. This can beshown or described using different ways such

as: table, arrow diagram, or by graphs.Function on the other hand is like analogy inour Language subject. The first object is inconnection with the second word itcorresponds.


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Exponent

Exponential Equation

Asymptote

Base

Inequalities


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Exponential Equation has the same base, meanshaving the same exponents.Exponent - ( power index) a number placed as asuperscript to the right of another number or

quantity indicating the number of times thenumber or quantity is to be multiplied by itself.Base - The number that is going to be raised to apower.

Ex. 3 = 3^x x = 2 therefore, 3 is the base.Asymptote The line approaches but never touches

the x-axis.Inequalities -


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The graph is asymptotic to x-axis

Value is Increasing if b > 1

Value is Decreasing if 0


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ExponentialFunction

Law ofexponents

Asymptoticto x-axis

Increasingif b > 1

Decreasingif 0


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The word Exponential means extremelyrapid or fast. Using exponential function, wecan express the rapid growth of people,

biological organisms, and other specie. Justremember the Laws of Exponents, and youllget it right.


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Characteristics

Mantissa

Base

Exponent

Logarithmic Function


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Characteristics - The part of a logarithm to the base10 that is to the left of the decimal point. ( .456are the characteristics below in the given.)Mantissa - The decimal part of a logarithm.

Ex. 3.456 (3 is the mantissa)Base - The number that is going to be raised to apower.Exponent - ( power index) a number placed as asuperscript to the right of another number orquantity indicating the number of times thenumber or quantity is to be multiplied by itself.


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Logarithmic Function For all positive realnumbers x and b, b is not equal to 1, there is areal number y, such that y = log b.

Log function is the inverse of exponentialfunction./It is asymptotic to y-axis

LAWS OF LOGARITHM:I. Logb^M = logb^N, then M=nII. Log (subscript)b (base)b ^m = m b^m = m


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b^ logb^m = mLog(subscript)b (base) b = 1Log b^1 = 0

Product Law:logb^MN = logb M +logbNQuotient Law:log (subscript)b M/N = log(subscript)b M-log(subscript)bNPower Law:

Log (subscript)b X^p = Plog(subscript)X


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Natural Logarithm The Logarithm of anumber to the base e.

Log e ^x = ln x

Change of base:Log b ^x = log x /log b


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Logarithms

Asymptoticto y-axis

Natural Log

Laws of Log

Log e ^x = ln x

Log b^1 = 0


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Logarithm Function is the inverse of theExponential Function. In the logarithmicfunction y log (subscript)a x, a>0 and a is not

equal to 1. Its domain is the set of all positivereal numbers. It can be expressed throughtables and graphs.


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Linear Function


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Linear FunctionlineSlopeinterceptVLT- Vertical Line Test


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Linear Function is a function of the form f(x)=mx+bLine is a segment that extends in both directions

Slope steepness, vertical change over horizontalchange, or simply, rise over run.intercept - two lines intersect each other.VLT(Vertical Line Test) - A test use to determine ifa relation is a function, and a relation is a functionif there are no vertical lines that intersectthe graph at more than one point.


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Point Slope Form: Two-point slope formSlope Intercept form Intercept FormStandard Form


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Vertical line UND- Vertical Line Test

Horizontal Line slope = 0Rise over o = UND


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Lines are everywhere, and linear Functionsplay an important part especially inconstructing infrastructures. Linear functions

are actually models of relations that showequal changes in the independent variable todependent variable.


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Trigonometric

Functions


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S-O-HC-A-HT-O-AOppositeHypotenuseAdjacent


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Sine sinCosine cosTangent tan

Cosecant cscSecant secCotangent cot

Opposite - the opposite/ other side of the triangle.Hypotenuse longest side of the triangleAdjacent the line in the triangle near the theta orangle.


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sin = Opposite/HypotenuseReciprocal: Csc = H/OCos = Adjacent/HypotenuseReciprocal: sec = H/ATan = Opposite/ AdjacentReciprocal: cot = A/O

Pythagorean Theorem : c^2 = a^2 + b ^2For special Triangles:45-45-90 degrees

30-60-60 degrees


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TrigonometricFunctionsSOH-CAH-TOA

SpecialTriangles

30-60-9045-45-90


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45-45-90 and 30-60-90 are used in specialtriangles. To solve the problems, say the thetais asked, we use SOH-CAH-TOA and their

reciprocals.


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CIRCULAR

FUNCTIONS


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SOHCAHTOAvertexTerminal sideArc

Initial sideRadius


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Pi - A transcendental number, approximately3.14159 and represented by the symbol Terminal side the end position of the ray/ line ofits rotation.Arc - A portion of the circumference of a circleInitial side - the starting position of the ray/ lineof its rotation.

Radius - A line from the center of a circle to a point on thecircle.

Vertex the endpoint of the two lines/ rays.Circumference - The distance around the edge of a circle


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CircularFunctions

Radius

Pi

SOHCAHTOA

Arc

Terminal/ initial

side


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Wheel, pizzas crust, tip of a glass, all of thoseare round shaped. At the ancient times, peopleinitially studied triangles ,but after time has

passed by, they have found out that there canbe triangles in a circle, thus, the beginning ofCircular Function.


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Trigonometric

Identities


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SOHCAHTOARadiusTheta


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sin = Opposite/HypotenuseReciprocal: Csc = H/OCos = Adjacent/Hypotenuse

Reciprocal: sec = H/ATan = Opposite/ AdjacentReciprocal: cot = A/O

Radius - Radius - A line from the center of acircle to a point on the circle.Theta a Greek alphabet ,usually used torepresent a side of the angle.


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COT

TrigonometricIdentities

SIN

COS

TAN

SEC

COT

CSC


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Trigonometric identities are equalities thatinvolve trigonometric functions and are truefor every single value of the

occurring variables. These identities are usefulwhenever expressions involving trigonometricfunctions need to be simplified.


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By: Jhobel LaurenteSubmitted to: Sir Noli DO. Rodriguez

IV-Cygnus

2011-2012

math your concept

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