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Examples for combining function transformations

Grade 12 Math: Master Advanced Concepts & Skills

Demonstrate an understanding of angles in standard position, expressed in degrees and radians

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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

Apply translations and stretches to the graphs and equations of functions

Combining transformations of functions

Demonstrate an understanding of the effects of reflections on the graphs of functions and their related equations

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

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

Even and odd functions

Demonstrate an understanding of inverses of relations

One to one functions

Finding inverse trigonometric function from its graph

Evaluating inverse trigonometric functions

Finding inverse reciprocal trigonometric function from its graph

Inverse reciprocal trigonometric function: finding the exact value

Inverse Reciprocal Trigonometric Function: Finding the Exact Value

Inverse functions

Demonstrate an understanding of logarithms

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

Evaluating logarithms using change-of-base formula

Converting from exponential form to logarithmic form

Demonstrate an understanding of the product, quotient and power laws of logarithms

Solving logarithmic equations

Product rule of logarithms

Quotient rule of logarithms

Combining product rule and quotient rule in logarithms

Evaluating logarithms using logarithm rules

Graph and analyze exponential and logarithmic functions

Graphing exponential functions

Graphing transformations of exponential functions

Finding an exponential function given its graph

Graphing logarithmic functions

Finding a logarithmic function given its graph

Solve problems that involve exponential and 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

Demonstrate an understanding of factoring polynomials of degree greater than 2

Polynomial long division

Polynomial synthetic division

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

Graph and analyze polynomial functions

Descartes&apos; rule of signs

Descartes' Rule of Signs

Descartes' rule of signs

Descartes" rule of signs

Polynomial functions

Recognizing a Polynomial Function

Characteristics of polynomial graphs

Determining the equation of a polynomial function

Applications of polynomial functions

Multiplicities of polynomials

Imaginary zeros of polynomials

Solving polynomial inequalities

Fundamental theorem of algebra

Graph and analyze radical functions

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

Develop and apply the equation of the unit circle

Unit circle

Graph and analyze rational functions

What is a rational function?

Point of discontinuity

Slant asymptote

Determining the Equation of a Slant Asymptote Using Long Division

Determining the Equation of a Slant Asymptote Using Synthetic Division

Solving rational equations

Solving rational inequalities

Solving Rational Inequalities With Two Fractions

Vertical asymptote

Horizontal asymptote

Horizontal Asymptote

Graphs of rational functions

Apply the fundamental counting principle to solve problems

Fundamental counting principle

Fundamental Counting Principle Involving Restrictions

Determine the number of permutations of n elements taken r at a time to solve problems

Factorial notation

Path counting problems

Permutations

Determine the number of combinations of n different elements taken r at a time to solve problems

Combinations

Problems involving both permutations and combinations

Permutation vs. Combination

Expand powers of a binomial in a variety of ways, including using the binomial theorem

Pascal's triangle

Pascal's Triangle

Pascal"s Triangle

Pascal"s triangle

Binomial theorem

Solve problems using the six trigonometric ratios for angles expressed in radians and degrees

Use sine ratio to calculate angles and sides (Sin = o / h)

Use cosine ratio to calculate angles and sides (Cos = a / h)

Combination of SohCahToa questions

Use tangent ratio to calculate angles and sides (Tan = o / a)

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

ASTC rule in trigonometry

Graph and analyze the trigonometric functions sine, cosine and tangent to solve problems

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

Determining trigonometric functions given their graphs

Ferris wheel trig problems

Tides and water depth trig problems

Spring (simple harmonic motion) trig problems

Solve, algebraically and graphically, first and second degree trigonometric equations with the domain expressed in degrees and radians

Solving first degree trigonometric equations

Solving second degree trigonometric equations

Solving trigonometric equations involving multiple angles

Determining non-permissible values for trig expressions

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

Prove trigonometric identities, using various trigonometric identities

Quotient identities and reciprocal identities

Pythagorean identities

Sum and difference identities

Sum and Difference Identities

Double-angle identities

Cofunction identities

Demonstrate an understanding of operations on, and compositions of, functions

Function notation (advanced)

Composite functions

Adding functions

Subtracting functions

Multiplying functions

Dividing functions

We&apos;ve got you covered with our complete help for Grade 12 math, whether it&apos;s Ontario curriculum, <a href="https://www.alberta.ca/writing-diploma-exams.aspx">Diploma exam</a> (Alberta), <a href="http://www.edu.gov.mb.ca/k12/assess/tests/index.html">Provincial test</a> (Manitoba) or <a href="https://www.saskatchewan.ca/residents/education-and-learning/departmental-exams">Departmental exam</a> (Saskatchewan).

Aligned with your class or textbook, you will get grade 12 math help on topics like Trigonometric identities, Vectors, Permutations and Combinations, Matrices, Polynomial functions and so many more. Learn the concepts with our video tutorials that show you step-by-step solutions to even the hardest grade 12 math questions. Then, strengthen your understanding with tons of grade 12 math practice. 

All our lessons are taught by experienced Grade 12 math teachers. Let&apos;s finish your homework in no time, and ACE that final.

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