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How to reflect a graph through the x-axis

NL.SO.3200PCBT1

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Fundamental counting principle

Fundamental Counting Principle Involving Restrictions

NL.SO.3200PCBT2

Factorial notation

Permutations

NL.SO.3200PCBT3

Combinations

Problems involving both permutations and combinations

NL.SO.3200PCBT4

Pascal's triangle

Pascal's Triangle

Pascal"s Triangle

Pascal"s triangle

Binomial theorem

NL.SO.3200RF1

Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

Reflection across the y-axis: y = f(-x)

Reflection across the x-axis: y = -f(x)

Transformations of functions: Horizontal stretches

Transformations of functions: Vertical stretches

NL.SO.3200RF10

Polynomial long division

Polynomial synthetic division

Polynomial functions

Recognizing a Polynomial Function

Remainder theorem

Finding the Remainder Using Synthetic Division and the Remainder Theorem

Factor theorem

Using the Factor Theorem to Test For Factors of a Polynomial

Rational zero theorem

Rational Zero Theorem

Factor by taking out the greatest common factor

Factor by taking out GCF

Factor by grouping

NL.SO.3200RF11

Characteristics of polynomial graphs

Determining the equation of a polynomial function

Multiplicities of polynomials

Imaginary zeros of polynomials

Curve sketching

NL.SO.3200RF12

Radical functions and transformations

Square root of a function

Solving radical equations

Solving Radical Equations Involving One Square Root Term

Solving Radical Equations Involving More than One Square Root Term

Basic radical functions

Basic Radical Function

Basic Radical Functions

NL.SO.3200RF2

Combining transformations of functions

NL.SO.3200RF3

Determining trigonometric functions given their graphs

NL.SO.3200RF4

Even and odd functions

NL.SO.3200RF5

One to one functions

Inverse functions

NL.SO.3200RF6

What is a logarithm?

Logarithms and Exponential Growth

Understanding Logarithms through Exponential Growth

Understanding Logarithms

Converting from logarithmic form to exponential form

Evaluating logarithms without a calculator

Common logarithms

Natural log: ln

NL.SO.3200RF7

Product rule of logarithms

Quotient rule of logarithms

Combining product rule and quotient rule in logarithms

Evaluating logarithms using logarithm rules

NL.SO.3200RF8

Graphing exponential functions

Graphing transformations of exponential functions

Graphing logarithmic functions

Finding a logarithmic function given its graph

NL.SO.3200RF9

Solving logarithmic equations

Solving exponential equations with logarithms

Exponential growth and decay by a factor

Exponential decay: Half-life

Exponential growth and decay by percentage

Finance: Compound interest

Finance: Compound Interest

Continuous growth and decay

Logarithmic scale: Richter scale (earthquake)

Logarithmic scale: pH scale

Logarithmic scale: dB scale

Finance: Future value and present value

Solving exponential equations using exponent rules

NL.SO.3200T1

Angle in standard position

Coterminal angles

Coterminal Angles

Reference angle

Converting between degrees and radians

Trigonometric ratios of angles in radians

Radian measure and arc length

NL.SO.3200T2

Unit circle

NL.SO.3200T3

Angle of elevation and depression

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

ASTC rule in trigonometry

NL.SO.3200T4

Sine graph: y = sin x

Cosine graph: y = cos x

Tangent graph: y = tan x

Cotangent graph: y = cot x

Secant graph: y = sec x

Cosecant graph: y = csc x

Graphing transformations of trigonometric functions

NL.SO.3200T5

Solving first degree trigonometric equations

Solving second degree trigonometric equations

Solving trigonometric equations involving multiple angles

NL.SO.3200T6

Quotient identities and reciprocal identities

Pythagorean identities

Sum and difference identities

Sum and Difference Identities

Double-angle identities

Solving trigonometric equations using pythagorean identities

Solving trigonometric equations using Pythagorean identities

Solving trigonometric equations using sum and difference identities

Solving trigonometric equations using double-angle identities

Cofunction identities

Advanced Mathematics 3200

Permutations Combinations and the Binomial Theorem

Relations and Functions

math

Intro

Ex. 1

The concept behind the reflections about the x-axis is basically the same as the reflections about the y-axis. The only difference is that, rather than the y-axis, the points are reflected from above the x-axis to below the x-axis, and vice versa.

Reflection across the x-axis: y = -f(x)