Functions
Function notation, evaluating functions, domain and range, and the vertical line test.
This page is a free outline of what the Functions lesson covers — it is not the lesson itself. The interactive lesson, practice, quizzes, and AI Tutor are inside the app.
This lesson covers
- Average Rate of Change The average rate of change is how much the output changes per unit of input between two points — the same as the slope of the line connecting them: (change in y) ÷ (change in x).
- Domain and Range
- Evaluating Functions Evaluating a function means finding its output for a given input: for f(x) = 2x + 1, f(4) = 2(4) + 1 = 9. Substitute the value for every x and simplify.
- Function Notation
- Function Tables A function table lists inputs and their outputs in two columns; you can read off values, spot the rule, or check whether each input has just one output.
- Identifying Functions A relationship is a function only if every input has exactly one output. Repeated x-values with different y-values break the rule — but outputs are allowed to repeat.
- Vertical Line Test The vertical line test checks a graph: if any vertical line crosses it more than once, it’s not a function, because that input would have two outputs.
Linked concepts (purple →) have a full explanation. Hover or tap a dotted ⓘ concept for a quick definition.
Inside the app, Functions comes with:
Read the explanation here for free — then practice it for real, with everything you need in one place.
24/7 AI Tutor — Ask anything and get a step-by-step explanation when you’re stuck — it teaches the concept, not just the answer. Every answer verified by three independent AIs.
- Practice sets — Open-book practice questions at your level, easiest-first — as many as you want, never scored.
- Quizzes — Scored quizzes on the whole lesson, so you know when you’re ready to move on.
- Skills Check — A concept-by-concept map of what you’ve mastered and what to focus on next.
- Worked examples — Tap the Brain Button on any example for alternative step-by-step explanations.
- Glossary — Plain-English definitions of every key term in the lesson.
- Formula sheet — The GED® & HiSET® formula sheets, on screen while you practice.
- Practice calculator — An on-screen calculator to build your calculator skills before test day.
- Math-fact flashcards — Quick drills for addition, multiplication, perfect squares, and square roots.
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