Algebra 1 Online!
Henrico County Public Schools, Virginia
Expressions and Operations

Equations and Inequalities



SOL Review Materials
The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including
a)   determining whether a relation is a function;
b)   domain and range; and
f)   making connections between and among multiple representations of functions including concrete, verbal, numeric, graphic, and algebraic.
Essential Knowledge and Skills 
  • Determine whether a relation, represented by a set of ordered pairs, a table, or a graph is a function.
  • Identify the domain, range, zeros, and intercepts of a function presented algebraically or graphically.
  • Represent relations and functions using concrete, verbal, numeric, graphic, and algebraic forms. Given one representation, students will be able to represent the relation in another form.
  • Detect patterns in data and represent arithmetic and geometric patterns algebraically.
Essential Understandings
  • A set of data may be characterized by patterns, and those patterns can be represented in multiple ways.
  • Graphs can be used as visual representations to investigate relationships between quantitative data.
  • Inductive reasoning may be used to make conjectures about characteristics of function families.
  • Each element in the domain of a relation is the abscissa of a point of the graph of the relation.
  • Each element in the range of a relation is the ordinate of a point of the graph of the relation.
  • A relation is a function if and only if each element in the domain is paired with a unique element of the range.
  • The values of f(x) are the ordinates of the points of the graph of f.
  • For each x in the domain of f, x is a member of the input of the function f, f(x) is a member of the output of f, and the ordered pair [x, f(x)] is a member of f.
  • Set builder notation may be used to represent domain and range of a relation.
Vertical Articulation
  1. SOL 7.12 - represent relationships with tables, graphs, rules, and words
  2. SOL 8.14 - make connections between any two representations (tables, graphs, words, rules)
  3. SOL 8.17 - identify domain, range, independent/dependent variable
  4. SOL AFDA.1 - investigate/analyze function (linear/quadratic exponential/log) families/ characteristics: a) continuity; b) local/abs max/min; c) domain/range; d) zeros; e) intercepts; f) intervals of increasing/ decreasing; g) end behaviors; h) asymptotes
  5. SOL AFDA.4 - transfer between/analyze multiple representations of functions (algebraic formulas/ graphs/ tables/words)
  6. SOL AII.7 - investigate/analyze functions (algebraically/ graphically) a) domain/range; b) zeros; c) x‐ and y‐intercepts; d) intervals of increasing/decreasing; e) asymptotes; f) end behavior; g) inverse of a function; h) composition of multiple functions
Instructional Materials
  1. VDOE ESS Lesson: Square Patios - Functions (PDF) - Connecting different representations of functions (Word)
  2. VDOE ESS Lesson: Functions 1 - Functions (PDF) - Investigating relations and functions (Word)
  3. Notes: Functions and Relations (doc) | Answer Key (pdf)
  4. Notes: Domain and Range (flipchart)
Real World Lessons
  1. VDOE ESS: Building Square Patios (pdf)
  2. Worksheet: Relations CW (doc)
  3. Worksheet: Relations HW (doc)
  4. ExamView Quiz: Relations
  1. SOL Mini Quiz
  1. JMU Pivotal Question:Domain and Range Scenarios (doc)
  2. JMU Pivotal Question:Domain of Functions (doc)
  3. JMU Pivotal Question: Range of Functions (doc)
  1. Video: PH Identifying Functions using a Mapping
  2. Video: PH Identifying Functions using a Vertical Line Test
  3. Video: PH Determining a Reasonable Domain and Range for a Situation
  4. Video: PH Modeling a Function Using Three View
Explore Learning
  1. Introduction to Functions - Determine if a relation is a function using the mapping diagram, ordered pairs, or the graph of the relation. Drag arrows from the domain to the range, type in ordered pairs, or drag points to the graph to add inputs and outputs to the relation.
  2. Linear Functions - Determine if a relation is a function from the mapping diagram, ordered pairs, or graph. Use the graph to determine if it is linear.
  1. Notes: Domain and Range - notes and interactives from
  2. Notes: Functions - notes on functions, function boxes, domain and range, and mappings at
Old Website Links
Common Core Standards