Functions and Graphs
Functions are one of the most important ideas in algebra because they describe how one quantity depends on another. Their graphs give a visual story: where the function is increasing or decreasing, where it crosses an axis, and how changes in the formula affect the shape. This topic hub helps you connect equations, tables, and graphs so you can move confidently between them.
Learning Path
Linear Equations
Refresh the core graphing ideas behind slope, intercepts, and patterns in relationships before moving on to fuller function graphs.
Open →Function Graph Explorer
Plot functions and inspect how the graph changes as you adjust formulas, parameters, and input values.
Open →Function Transformations Lab
Practice shifting, stretching, reflecting, and compressing graphs to see how algebraic changes affect the picture.
Open →Functions and Graphs Quick Reference
Keep these ideas handy while you work:
- A function assigns exactly one output to each input; the graph shows those input-output pairs as points.
- Use domain and range to describe what x-values are allowed and what y-values the function can produce.
- Look for intercepts, intervals where the graph rises or falls, and transformations like shifts, stretches, and reflections.
More Resources
Tools
Labs
Worksheets
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Explainers
Common Questions
What is the difference between a function and its graph?
A function is the rule or relationship itself, while the graph is the visual picture of that relationship on a coordinate plane.
How do I tell what a graph is doing?
Check key features like intercepts, slope or curvature, and whether the graph is increasing, decreasing, shifted, stretched, or reflected.