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How to reflect a graph through the x-axis

Grade 12 Math: Master Advanced Concepts & Skills

Geometric explorations

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Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Conics - Parabola

Conics - Circle

Conics - Ellipse

Conics - Hyperbola

Graphical representations of polynomial, logarithmic, exponential, and sinusoidal functions

Graphing exponential functions

Graphing transformations of exponential functions

Graphing logarithmic functions

Sine graph: y = sin x

Cosine graph: y = cos x

Tangent graph: y = tan x

Regression analysis

Equation of the best fit line

Combinatorics

One to one functions

Combining transformations of functions

Fundamental counting principle

Fundamental Counting Principle Involving Restrictions

Factorial notation

Path counting problems

Permutations

Combinations

Problems involving both permutations and combinations

Pascal's triangle

Pascal's Triangle

Pascal"s Triangle

Pascal"s triangle

Function notation (advanced)

Composite functions

Adding functions

Subtracting functions

Multiplying functions

Dividing functions

Operations of Functions – In a Nutshell

Inverse functions

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

Operations with functions

Inequalities of combined functions

Inequalities of Combined Functions

Even and odd functions

Difference quotient: applications of functions

Odds, probability, and expected value

Applications of linear relations

What is a polynomial?

Classifying Polynomials

Introduction to probability

Identify the Probability — Word Problem

Compound Probability

Reading Probability Models

Probability

Organizing outcomes

Calculating Outcomes

Probability of independent events

Comparing experimental and theoretical probability

comparing experimental and theoretical probability

Polynomial components

Multiplying monomial by monomial

Multiply a Monomial by a Monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

Reading and drawing Venn diagrams

Probability with Venn diagrams

Financial planning

Simple interest

Simple Interest — Word Problem

Basic Concepts of Simple Interest – Word Problem

Borrowing Money for More Than One Year  – Word Problem

Investigate the Advantages of Borrowing Money  – Word Problem

Binomial theorem

Finance: Compound interest

Finance: Compound Interest

Finance: Future value and present value

Permutation vs. Combination

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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. 

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Foundations of Mathematics 12

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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)