Algebraic Reasoning

Master Algebraic Reasoning

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Texas Algebraic Reasoning Help: Master Concepts FastHelp

ID	Standard	StudyPug Topic
TX.AR.2.A	Determine the patterns that identify the relationship between a function and its common ratio or related finite differences as appropriate, including linear, quadratic, cubic, and exponential functions	Arithmetic sequences Geometric sequences Understand relations between x- and y-intercepts Domain and range of a function Identifying functions Function notation Rate of change Applications of linear relations

TX.AR.2.B

Classify a function as linear, quadratic, cubic, and exponential when a function is represented tabularly using finite differences or common ratios as appropriate

Relationship between two variables

Characteristics of quadratic functions

Representing patterns in linear relations

Reading linear relation graphs

Solving linear equations by graphing

Understanding graphs of linear relationships

Understanding tables of values of linear relationships

Applications of linear relationships

TX.AR.2.C

Determine the function that models a given table of related values using finite differences and its restricted domain and range

Graphing linear functions using table of values

Graphing quadratic functions: General form VS. Vertex form

Graphing linear functions using x- and y-intercepts

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

TX.AR.2.D

Determine a function that models real-world data and mathematical contexts using finite differences such as the age of a tree and its circumference, figurative numbers, average velocity, and average acceleration

Word problems of graphing linear functions

Applications of quadratic functions

Unknown number related questions in linear equations

Distance and time related questions in linear equations

Rectangular shape related questions in linear equations

TX.AR.3.A

Compare and contrast the key attributes of a set of functions such as linear, quadratic, and exponential

Slope intercept form: y = mx + b

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

Graphing exponential 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

TX.AR.3.B

Compare and contrast the key attributes of a function and its inverse when it exists

Inverse functions

Combining transformations of functions

Even and odd functions

TX.AR.3.C

Verify that two functions are inverses of each other tabularly and graphically

Adding functions

Subtracting functions

Multiplying functions

Dividing functions

TX.AR.3.D

Represent a resulting function tabularly, graphically, and symbolically when functions are combined or separated using arithmetic operations

Operations with functions

TX.AR.3.E

Model a situation using function notation when the output of one function is the input of a second function

Composite functions

Function notation (advanced)

One to one functions

TX.AR.3.F

Compare and contrast a function and possible functions that can be used to build it

Difference quotient: applications of functions

TX.AR.4.A

Connect tabular representations to symbolic representations when adding, subtracting, and multiplying polynomial functions

Adding and subtracting polynomials

Multiplying polynomial by polynomial

Characteristics of polynomials

Equivalent expressions of polynomials

Multiplying and dividing monomials

Multiplying polynomials by monomials

Dividing polynomials by monomials

TX.AR.4.B

Compare and contrast the results when adding two linear functions and multiplying two linear functions

Inequalities of combined functions

TX.AR.4.C

Determine the quotient of a polynomial function of degree three and of degree four when divided by a polynomial function of degree one and of degree two when represented tabularly and symbolically

Polynomial long division

Polynomial synthetic division

TX.AR.4.D

Determine the linear factors of a polynomial function of degree two and of degree three when represented symbolically and tabularly and graphically where appropriate

Factoring polynomials: ax^2 + bx + c

Rational zero theorem

Common factors of polynomials

Factoring polynomials by grouping

Solving polynomials with unknown coefficients

Solving polynomials with unknown constant terms

Factoring polynomials: x^2 + bx + c

Applications of polynomials: x^2 + bx + c

Solving polynomials with the unknown

Factoring perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

TX.AR.5.A

Add and subtract matrices

Adding and subtracting matrices

TX.AR.5.B

Multiply matrices

Matrix multiplication

TX.AR.5.C

Multiply matrices by a scalar

Scalar multiplication of matrices

TX.AR.5.D

Represent and solve systems of two linear equations arising from mathematical and real-world situations using matrices

System of linear equations

Representing a linear system as a matrix

Solving a linear system with matrices using Gaussian elimination

TX.AR.5.E

Represent and solve systems of three linear equations arising from mathematical and real-world situations using matrices and technology

Solving 3 variable systems of equations by substitution

Solving 3 variable systems of equations by elimination

The determinant of a 2 x 2 matrix

The determinant of a 3 x 3 matrix (General & Shortcut Method)

The Inverse of a 2 x 2 matrix

The inverse of 3 x 3 matrices with matrix row operations

The inverse of 3 x 3 matrix with determinants and adjugate

2 x 2 invertible matrix

Solving linear systems using Cramer's Rule

Solving linear systems using 2 x 2 inverse matrices

TX.AR.6.B

Solve equations arising from questions asked about functions that model real-world applications, including linear and quadratic functions

Introduction to linear equations

Solving quadratic equations by factoring

TX.AR.6.C

Approximate solutions to equations arising from questions asked about exponential, logarithmic, square root, and cubic functions that model real-world applications

Solving exponential equations using exponent rules

Solving logarithmic equations

Solving radical equations

TX.AR.7.A

Represent domain and range of a function using interval notation, inequalities, and set notation

Set notation

Set builder notation

Intersection and union of 2 sets

Intersection and union of 3 sets

TX.AR.7.C

Determine the accuracy of a prediction from a function that models a set of data compared to the actual data

Regression analysis

TX.AR.7.D

Determine an appropriate function model, including linear, quadratic, and exponential functions, for a set of data arising from real-world situations using finite differences and average rates of change

Equation of the best fit line

Complete Texas Algebraic Reasoning Coverage

Algebraic Reasoning Lessons

95

Video Explanations

705

Practice Problems

803

Texas Standards

100% Aligned

Why Texas Algebraic Reasoning Students Love StudyPug

STAAR EOC Preparation

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Success Stories

Matrix operations confused me completely. The step-by-step videos made everything clear. Aced my chapter test with a 92%.

Jordan Lee

Polynomial division was my worst topic. Photo search found the exact lessons I needed. Raised my grade from C to A- in one semester.

Taylor Nguyen

Frequently Asked Questions

Get answers to common questions about Algebraic Reasoning on StudyPug

What does Algebraic Reasoning coverage include?

Complete Texas Algebraic Reasoning curriculum with video lessons on functions, matrices, polynomials, and modeling. Includes practice problems, step-by-step solutions, and progress tracking for every topic.

How does photo search work?

Take a photo of any Algebraic Reasoning problem, and StudyPug finds the exact lesson teaching that concept. It's like having a personal tutor who knows exactly what you need.

Are the teachers certified Texas educators?

Yes! Our teachers are certified Texas educators who understand Algebraic Reasoning curriculum and create lessons specifically for Texas TEKS standards.

Can I use StudyPug on my phone or tablet?

Absolutely! StudyPug works on desktop, tablet, and mobile. Your progress syncs automatically so you can learn anywhere, anytime.

How will StudyPug help me prepare for the STAAR EOC exam?

We include STAAR-style practice questions for every Algebraic Reasoning topic and teach the exact concepts tested on the exam. Students report significantly improved test scores and confidence.

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Master Algebraic Reasoning

Watch algebra videos, practice with step-by-step solutions

Why Algebraic Reasoning Students Choose StudyPug

Search with Photo

Expert Video Teaching

Unlimited Practice

How Texas Students Use StudyPug

1

Select Grade Level

2

Get Unstuck

3

Practice & Master

4

See Results

Texas Algebraic Reasoning Help: Master Concepts FastHelp

ID

Standard

StudyPug Topic

TX.AR.2.A

Determine the patterns that identify the relationship between a function and its common ratio or related finite differences as appropriate, including linear, quadratic, cubic, and exponential functions

TX.AR.2.B

Classify a function as linear, quadratic, cubic, and exponential when a function is represented tabularly using finite differences or common ratios as appropriate

TX.AR.2.C

Determine the function that models a given table of related values using finite differences and its restricted domain and range

TX.AR.2.D

Determine a function that models real-world data and mathematical contexts using finite differences such as the age of a tree and its circumference, figurative numbers, average velocity, and average acceleration

TX.AR.3.A

Compare and contrast the key attributes of a set of functions such as linear, quadratic, and exponential

TX.AR.3.B

Compare and contrast the key attributes of a function and its inverse when it exists

TX.AR.3.C

Verify that two functions are inverses of each other tabularly and graphically

TX.AR.3.D

Represent a resulting function tabularly, graphically, and symbolically when functions are combined or separated using arithmetic operations

TX.AR.3.E

Model a situation using function notation when the output of one function is the input of a second function

TX.AR.3.F

Compare and contrast a function and possible functions that can be used to build it

TX.AR.4.A

Connect tabular representations to symbolic representations when adding, subtracting, and multiplying polynomial functions

TX.AR.4.B

Compare and contrast the results when adding two linear functions and multiplying two linear functions

TX.AR.4.C

Determine the quotient of a polynomial function of degree three and of degree four when divided by a polynomial function of degree one and of degree two when represented tabularly and symbolically

TX.AR.4.D

Determine the linear factors of a polynomial function of degree two and of degree three when represented symbolically and tabularly and graphically where appropriate

TX.AR.5.A

Add and subtract matrices

TX.AR.5.B

Multiply matrices

TX.AR.5.C

Multiply matrices by a scalar

TX.AR.5.D

Represent and solve systems of two linear equations arising from mathematical and real-world situations using matrices

TX.AR.5.E

Represent and solve systems of three linear equations arising from mathematical and real-world situations using matrices and technology

TX.AR.6.B

Solve equations arising from questions asked about functions that model real-world applications, including linear and quadratic functions

TX.AR.6.C

Approximate solutions to equations arising from questions asked about exponential, logarithmic, square root, and cubic functions that model real-world applications

TX.AR.7.A

Represent domain and range of a function using interval notation, inequalities, and set notation

TX.AR.7.C

Determine the accuracy of a prediction from a function that models a set of data compared to the actual data

TX.AR.7.D

Determine an appropriate function model, including linear, quadratic, and exponential functions, for a set of data arising from real-world situations using finite differences and average rates of change

Complete Texas Algebraic Reasoning Coverage

95

705

803

100% Aligned

See All Topics

Why Texas Algebraic Reasoning Students Love StudyPug

STAAR EOC Preparation

Certified Teachers

Learn Anywhere

Success Stories

Matrix operations confused me completely. The step-by-step videos made everything clear. Aced my chapter test with a 92%.

Polynomial division was my worst topic. Photo search found the exact lessons I needed. Raised my grade from C to A- in one semester.