Will this help with my child's Algebraic Reasoning homework?

Yes. StudyPug covers every Texas TEKS Algebraic Reasoning topic, including finite differences, polynomial operations, and matrix systems, with step-by-step video lessons and practice problems your student can use the same night homework is assigned.

How long are the Algebraic Reasoning video lessons?

Most video lessons run between five and fifteen minutes, focusing on one concept at a time. Students can pause, rewind, and rewatch at any point, making it easy to keep up with classwork or review a topic before a test.

Is there a state test for Algebraic Reasoning in Texas?

Texas Algebraic Reasoning is an elective course and does not have a dedicated STAAR end-of-course exam. Students taking Algebra I will sit the STAAR Algebra I EOC, which covers related linear and quadratic content assessed under Texas TEKS.

Can my child use StudyPug on a tablet or phone?

Yes. StudyPug works on tablets, phones, laptops, and desktop computers. Your student can switch between devices at any time, so they can practice at home, at school, or on the go without losing their progress.

Can I try StudyPug before paying?

Yes. StudyPug offers free sample lessons so you can see the content before committing. Every paid plan also comes with a 30-day money-back guarantee, so you can sign up with confidence.

TX High School Algebraic Reasoning Curriculum

Give your student the support they need for Texas Algebraic Reasoning. Our lessons follow Texas TEKS, covering functions, polynomial operations, matrices, and real-world data modeling.

TX High School Algebraic Reasoning Curriculum

IDStrand & ExpectationStudyPug Topic

TX.AR.2.ADetermine 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.BClassify 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.CDetermine 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.DDetermine 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
- Money related questions in linear equations
- 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.ACompare 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.BCompare 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.CVerify that two functions are inverses of each other tabularly and graphically
- Adding functions
- Subtracting functions
- Multiplying functions
- Dividing functions
TX.AR.3.DRepresent a resulting function tabularly, graphically, and symbolically when functions are combined or separated using arithmetic operations
- Operations with functions
TX.AR.3.EModel 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.FCompare and contrast a function and possible functions that can be used to build it
- Difference quotient: applications of functions
TX.AR.4.AConnect 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.BCompare and contrast the results when adding two linear functions and multiplying two linear functions
- Inequalities of combined functions
TX.AR.4.CDetermine 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.DDetermine 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.AAdd and subtract matrices
- Adding and subtracting matrices
TX.AR.5.BMultiply matrices
- Matrix multiplication
TX.AR.5.CMultiply matrices by a scalar
- Scalar multiplication of matrices
TX.AR.5.DRepresent 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.ERepresent 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.BSolve 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.CApproximate 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.ARepresent 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.CDetermine the accuracy of a prediction from a function that models a set of data compared to the actual data
- Regression analysis
TX.AR.7.DDetermine 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

Algebraic Reasoning

About High School Texas Algebraic Reasoning

Texas Algebraic Reasoning follows the Texas TEKS, organized around functions and their behaviors, polynomial and matrix operations, and data modeling. Students classify linear, quadratic, cubic, and exponential functions using finite differences, perform arithmetic on polynomials and matrices, and solve systems of equations. StudyPug provides step-by-step lessons, practice problems, and worked examples aligned to these Texas standards so students can build confidence at their own pace.

Strands: functions and finite differences, polynomial operations, matrix algebra, and real-world data modeling
Video lessons for every Algebraic Reasoning topic, aligned to Texas TEKS
Practice problems and worked examples covering functions, polynomials, and matrices
Tools to estimate, solve, and model real-world situations using linear, quadratic, and exponential functions

Curriculum topics by strand

Find lessons and practice for every Texas Algebraic Reasoning strand, aligned to the Texas TEKS.

Topic includes:

Practice

Video

Quiz

Strand & Expectation

StudyPug Topic

Texas High School Algebraic Reasoning Topics

Functions and finite differences: Classifying and comparing linear, quadratic, cubic, and exponential functions using common ratios and finite differences, including inverse functions and function composition.
Polynomial operations: Adding, subtracting, multiplying, and dividing polynomial functions; connecting tabular and symbolic representations; identifying linear factors of degree-two and degree-three polynomials.
Matrix algebra: Adding, subtracting, multiplying, and scaling matrices; representing and solving systems of two and three linear equations using matrices and technology.
Real-world data modeling: Using finite differences and average rates of change to select appropriate function models; comparing mathematical and reasonable domain and range; evaluating prediction accuracy against actual data.

How StudyPug Helps Texas High School Algebraic Reasoning Students

When a student gets stuck on classifying a function from a table or setting up a matrix equation, StudyPug provides short, focused video lessons that walk through each step at a pace the student controls. Practice problems follow each lesson so students can check their understanding right away.

StudyPug covers the full Texas Algebraic Reasoning course from finite differences and function inverses through polynomial arithmetic and real-world modeling, giving students a reliable place to get unstuck any night of the week.

Aligned to Texas High School Algebraic Reasoning Curriculum

Every lesson and practice problem on StudyPug is built around the Texas TEKS for Algebraic Reasoning, so the content your student works through matches exactly what is taught in their Texas classroom, from representing domain and range in interval notation to approximating solutions for exponential and logarithmic functions in real-world contexts.

Ready to put your TX High School Algebraic Reasoning skills to the test?

Jump into practice questions for every TX Algebraic Reasoning topic - with instant feedback and step-by-step video solutions when you get stuck.

Start Practicing

Written by the StudyPug Math Team

Last updated June 5, 2026

3 M+

students

★★★★★

4.8 average

92%

improve grades