8th Grade Math

Algebra foundations, geometry, and mathematical modeling for eighth grade students.

Linear Equations and ExpressionsFunctions and GraphsIntro to Geometry: Angles and Shapes
Systems of EquationsPythagorean TheoremVolume and Surface Area of 3D Shapes
Budgeting and Saving with AlgebraGeometry in Construction and DesignModeling and Interpreting Data
Breaking Down Word ProblemsChecking Your Work and Estimating
Linear Equations and...Functions and GraphsIntro to Geometry: A...Systems of EquationsPythagorean TheoremVolume and Surface A...Budgeting and Saving...Geometry in Construc...Modeling and Interpr...Breaking Down Word P...Checking Your Work a...
Basic Concepts

Functions and Graphs

What Is a Function?

A function is a special rule that matches each input to exactly one output. You can think of it like a machine: put in a number, and it gives you a result.

Graphing Functions

Functions can be shown as graphs on the coordinate plane. For example, the function \(y = 2x + 1\) makes a straight line.

How to Graph:

  1. Make a table of values for \(x\) and \(y\).
  2. Plot the points on the plane.
  3. Connect them to see the pattern!

Reading Graphs

Graphs help you see how things change. A steep line means a big change; a flat line means a small change.

Real-Life Uses

Graphs are everywhere! They show how your savings grow, how fast you run, or how temperatures change during the day.

Examples

  • The function \(y = 3x\) means if \(x = 2\), then \(y = 6\).

  • Graph the points (0,1), (1,3), (2,5) for \(y = 2x + 1\).

In a Nutshell

Functions connect inputs to outputs, and graphs help us picture these relationships.

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Intro to Geometry: Angles and Shapes