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Master Graphing Reciprocals of Linear Functions | Easy Guide

Understand absolute value of real numbers

Absolute value functions

Expressing an Absolute Value Linear Function as a Piecewise Function

Expressing an Absolute Value Quadratic Function as a Piecewise Function

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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"

Solve problems with operations on radicals and radical expressions

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

Solve 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

Partial fraction decomposition

Simplifying rational expressions and restrictions

Simplifying complex fractions

Perform operations on rational expressions

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

Solve problems involving rational equations

Solving rational equations

Applications of rational equations

Factor polynomials

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 in different forms

Characteristics of quadratic functions

Transformations of quadratic functions

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

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

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

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

Solve problems involving quadratic equations

Introduction to quadratic functions

Applications of quadratic functions

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

Completing the square

Completing the Square

Solve systems of linear-quadratic and quadratic-quadratic equations

Solving polynomial equations by iteration

System of linear equations

System of linear-quadratic equations

System of quadratic-quadratic equations

Solve linear and quadratic inequalities

Solving quadratic inequalities

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

Analyze arithmetic and geometric sequences and series

What is linear programming?

Finding Optimal Values Given Constraints In Slope-Intercept Form

Finding Optimal Values Given Constraints In Standard Form

Arithmetic sequences

Arithmetic series

Arithmetic series formula

Geometric sequences

Geometric series

Geometric Series

Infinite geometric series

Graph and analyze reciprocal functions

Graphing reciprocals of linear functions

Graphing reciprocals of quadratic functions

Understand angles in standard position

Angle in standard position

Coterminal angles

Coterminal Angles

Reference angle

Solve problems using trigonometric ratios for angles from 0° to 360°

Unit circle

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

ASTC rule in trigonometry

Solve problems using cosine law and sine law including ambiguous case

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

Pre-Calculus 11 (MAT521B)

Algebra and Number

Relations and Functions

math

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