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Master Graphing Reciprocals of Linear Functions | Easy Guide

Grade 11 Math: Master Advanced Concepts & Skills

Demonstrate an understanding of the absolute value of real numbers

Upper and lower bound

Upper and Lower Bound

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Absolute value functions

Expressing an Absolute Value Linear Function as a Piecewise Function

Expressing an Absolute Value Quadratic Function as a Piecewise Function

Solving absolute value equations

Solving absolute value inequalities

Solving Absolute Value Inequalities Involving "less than"

Solving Absolute Value Inequalities Involving "greater than"

Recognizing Absolute Value Inequalities with "No Solution" or "All Real Numbers"

Factor polynomial expressions of various forms

Factoring difference of cubes

Factoring sum of cubes

Factor by taking out the greatest common factor

Factor by taking out GCF

Factor by grouping

Factoring difference of squares: \(x^2 - y^2\)

Factoring difference of squares: <katex>x^2 - y^2</katex>

Factoring difference of squares: x^2 - y^2

Factoring trinomials

Factoring Trinomials

Analyze quadratic functions of the form y = a(x - p)² + q and determine their characteristics

Introduction to quadratic functions

Transformations of quadratic functions

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Converting general form into vertex form by applying the vertex formula

Vertex Formula Application

Finding the quadratic functions for given parabolas

Quadratic function in vertex form: y = a(x-p)^2 + q

Analyze quadratic functions of the form y = ax² + bx + c to identify characteristics of the corresponding graph

Solving polynomial equations by iteration

Characteristics of quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Graphing quadratic functions: General form VS. Vertex form

Applications of quadratic functions

Completing the square

Completing the Square

Solve problems that involve quadratic equations

Solving 3 variable systems of equations by substitution

Solving 3 variable systems of equations by elimination

Solving quadratic equations by factoring

Solving quadratic equations by completing the square

Using quadratic formula to solve quadratic equations

Solving a quadratic equation with TWO REAL SOLUTIONS

Solving a quadratic equation with TWO COMPLEX SOLUTIONS

Nature of roots of quadratic equations: The discriminant

Applications of quadratic equations

System of linear equations

Solve, algebraically and graphically, problems that involve systems of linear-quadratic and quadratic-quadratic equations in two variables

What is linear programming?

Finding Optimal Values Given Constraints In Slope-Intercept Form

Finding Optimal Values Given Constraints In Standard Form

Linear programming word problems

System of linear-quadratic equations

System of quadratic-quadratic equations

Solve problems that involve linear and quadratic inequalities in two variables

Graphing linear inequalities in two variables

Graphing quadratic inequalities in two variables

Graphing systems of quadratic inequalities

Graphing systems of linear inequalities

Applications of inequalities

Solve problems that involve quadratic inequalities in one variable

Solving quadratic inequalities

Sigma notation

Analyze arithmetic sequences and series to solve problems

Arithmetic sequences

Arithmetic series

Arithmetic series formula

Arithmetic mean vs. Geometric mean

Analyze geometric sequences and series to solve problems

What is a rational function?

Point of discontinuity

Geometric sequences

Geometric series

Geometric Series

Infinite geometric series

Vertical asymptote

Horizontal asymptote

Horizontal Asymptote

Solve problems that involve operations on radicals and radical expressions with numerical and variable radicands

Conversion between entire radicals and mixed radicals

Adding and subtracting radicals

Combining Like Radicals

Adding and Subtracting Radicals

Multiplying radicals

Multiplying Radicals

Operations with radicals

Operations with Radicals

Adding radicals

Subtracting radicals

Multiplying and dividing radicals

Dividing radicals

Rationalize the denominator

Graph and analyze reciprocal functions (limited to the reciprocal of linear and quadratic functions)

Graphing reciprocals of linear functions

Graphing reciprocals of quadratic functions

Solve problems that involve radical equations (limited to square roots)

Solving radical equations

Solving Radical Equations Involving One Square Root Term

Solving Radical Equations Involving More than One Square Root Term

Determine equivalent forms of rational expressions (limited to numerators and denominators that are monomials, binomials or trinomials)

Partial fraction decomposition

Simplifying rational expressions and restrictions

Perform operations on rational expressions (limited to numerators and denominators that are monomials, binomials or trinomials)

Adding and subtracting rational expressions

Adding and Subtracting Rational Expressions

Multiplying rational expressions

Multiplying Rational Expressions

Multiplying Rational Expressions in Factored Form

Dividing rational expressions

Dividing Rational Expressions

Dividing Rational Expressions in Factored Form

Simplifying complex fractions

Solve problems that involve rational equations (limited to numerators and denominators that are monomials, binomials or trinomials)

Solving rational equations

Applications of rational equations

Demonstrate an understanding of angles in standard position 0° to 360°

Angle in standard position

Coterminal angles

Coterminal Angles

Reference angle

Solve problems, using the three primary trigonometric ratios for angles from 0° to 360° in standard position

Unit circle

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (<b>A</b>ll <b>S</b>tudents <b>T</b>ake <b>C</b>alculus)

ASTC rule in trigonometry

Solve problems, using the cosine law and sine law, including the ambiguous case

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

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Intro

Intro to reciprocal functions: properties, invariant points, and asymptotes

Ex.1

Graphing the reciprocal of f(x) = 4x using five steps

Ex.2

Graphing the reciprocal of f(x) = x + 5 using the 5-step method

Ex.3

Graphing 1/(2x-1) using the five-step reciprocal method

Ex.4

Graphing the reciprocal of y = 1/2 - 5x using five steps

Ex.5

Graphing the reciprocal of y = 1/3 - x/9 using five steps

We know that taking the reciprocal of a very large number will grant us a very small number. Conversely, if we take the reciprocal of a very small number, we will obtain a very small number. What will happen if we take the reciprocal of a linear function? In this section, we will learn about the concept behind the reciprocal of a linear function, as well as how to graph it, while following the "5-steps Approach" noted below.

How to graph reciprocals of linear functions