Algebra I Foundations Competencies



1.Function and Relation Representation

Create and connect representations of various functions using graphs, patterns, equations, and

written/verbal expression.

Define and recognize the following relations and functions:

• Quadratic

• Absolute Value

• Linear

• Piece-wise

• Exponential

• Radical

• Linear Inequalities

• Quadratic Inequalities


Graph and sketch all functions and relations from a

• Table of values

• List of given properties

• Equation of a function

• Using intercepts

• Systems of Linear Inequalities


Determine an exact or suitable possibility for the equation of a function from a

• Table of values

• List of given properties

• Graph of a function


Create a table of values from a

• Graph of a function

• Equation of a function



Transformations of all functions graphically without a calculator or table of values

• Shifting horizontally and vertically

• Stretching and compressing vertically

• Reflections about the origin, x-axis, and y-axis


 2.Manipulate and Relate Expressions

Rewrite expressions in equivalent and related forms and solve equations and inequalities using

various techniques.

Solve equations and simplify expressions of all types.

• Use Order of Operations to simplify expressions

• Solve one, two and multi-step equations and inequalities

• Solve proportions

• Rewrite a formula for a specific variable

• Solve absolute value equations and inequalities

• Verbal/written description

• Direct and inverse variations

• Systems of equations

• Quadratic equations

• Radical equations

• Simplify integer exponents

• Operations with radicals

• Operations on polynomials

• Simplify rational expressions


3.Problem Solving

Collect, organize, analyze, and assess information and strategies to create, apply, explain, and

evaluate solutions.

Determine the following:

• Domain and range

• x-intercepts (roots, zeros) and y-intercepts

• where a function is increasing and decreasing

• vertex (of a quadratic)


Investigate and analyze real world applications pertaining to all mathematical situations.

• Linear equations

• Linear inequalities

• Absolute Value equations (tolerance)

• Systems of equations/inequalities

• Quadratic equations (maximize, minimize)

• Exponential equations


Apply the graphing calculator in order to recognize properties using an appropriate window.

Find a best fit model for a data set

• Using a graphing calculator

• By hand