GED® Algebra: Functions and Graphs
A focused GED® Mathematical Reasoning course on functions, graphs, slope, linear equations, coordinate interpretation, and graph-based reasoning. Students learn how to move between tables, rules, equations, and graphs; evaluate function notation; interpret slope as rate of change; graph lines and inequalities; compare functions; and recognize nonlinear patterns. Lessons use an academic style with clear definitions, worked examples, visual figures, common-misconception notes, and GED®-style practice.
📚 Course Curriculum
The coordinate plane is a precise map for numerical relationships. The horizontal axis is the x-axis, the vertical axis is the y-axis, and their crossing …
Open trial session →A table gives ordered pairs. Each row becomes one point on a graph. When the same rule is used for every row, the graph shows …
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A relation is any set of input-output pairs. A function is a special relation where each input has exactly one output. [[figure:function_machine A function is …
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Function notation is a compact way to name a rule. If. then \(f(4)\) means "the output of the function when the input is 4.". Evaluate …
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Slope measures how quickly \(y\) changes compared with \(x\). It is the ratio:. [[figure:slope_types Slope direction tells whether a line rises, falls, stays flat, or …
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Most GED® line questions use slope-intercept form:. Here \(m\) is the slope and \(b\) is the y-intercept, the point where the line crosses the y-axis. …
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Graph and table questions often ask for the equation of a line. A linear equation needs two pieces of evidence: slope and one point. The …
Open trial session →An intercept is where a graph crosses an axis. The y-intercept occurs where \(x=0\). The x-intercept occurs where \(y=0\). These points often have real-world meaning. …
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A system of equations is two or more equations considered at the same time. On a graph, the solution is the intersection point because that …
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A linear inequality in two variables describes a region of the coordinate plane, not just a line. [[figure:linear_inequality_shade For \(y>x+1\), the boundary is dashed and …
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GED® questions often ask students to compare two functions presented in different forms: an equation, a table, a graph, or a verbal description. To compare …
Open trial session →Not every relationship is linear. A linear function changes by equal differences and graphs as a line. A quadratic function has an \(x^2\) term and …
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Course Syllabus
This self-paced GED® Math course follows a 12-lesson sequence. Work through the modules in order so that each skill supports the next.
Course sequence
Module 1 - Lessons 1-4
- The Coordinate Plane as a Data Map
- From Tables to Graphs
- What Makes a Relation a Function
- Function Notation, Domain, and Range
Module 2 - Lessons 5-8
- Slope as Rate of Change
- Slope-Intercept Form and Graphing Lines
- Writing Linear Equations from Evidence
- Intercepts, Standard Form, and Graph Interpretation
Module 3 - Lessons 9-12
- Systems of Equations as Intersections
- Graphing Linear Inequalities
- Comparing Functions in Different Forms
- Nonlinear Patterns and Final Graph Strategy
Practice and completion
- Use worked examples and lesson practice to check understanding after each module.
- Review incorrect answers, explain the correction, and repeat weak skills.
- Complete the available mixed or final course practice to demonstrate readiness.
Course Outcomes
By the end of this course, learners will be able to:
- Explain and apply the mathematical ideas in The Coordinate Plane as a Data Map.
- Solve multi-step problems involving Function Notation, Domain, and Range and show a clear method.
- Interpret representations and check the reasonableness of work involving Writing Linear Equations from Evidence.
- Choose efficient strategies for unfamiliar questions related to Systems of Equations as Intersections.
- Combine skills from Nonlinear Patterns and Final Graph Strategy with earlier topics in mixed practice.
- Use feedback and answer explanations to diagnose and correct mistakes.
- Complete mixed, exam-style practice with clearer reasoning and greater independence.
📝 Practice Questions
52 interactive questions with instant feedback and explanations.
Enroll for free to unlock the full practice bank after the trial sessions.