Domain and Range
Every function has two important sets: the domain (all valid input values) and the range (all possible output values).
This is a free explanation of Domain and Range — a preview, not the full interactive lesson. The lesson, practice, quizzes, and AI Tutor are inside the app.
The domain is the complete set of valid input values — all the x-values the function will accept. For most GED functions like f(x) = 2x + 5, any real number works, so the domain is all real numbers.
The range is the complete set of output values the function can produce — all possible y-values. For f(x) = x², the smallest output is 0 (when x = 0), and squaring never gives a negative result, so the range is all numbers greater than or equal to 0.
Watch for restrictions. When a function has a square root, the expression inside must be greater than or equal to zero; when it has a fraction, the denominator cannot equal zero — those inputs are excluded from the domain.
Worked example
Find the domain of f(x) = √(2x − 6).
- The expression inside a square root can’t be negative, so set it greater than or equal to zero: 2x − 6 ≥ 0.
- Solve: add 6 to both sides to get 2x ≥ 6.
- Divide by 2: x ≥ 3.
- Check: f(3) = √0 = 0, which works; f(1) = √(−4) is undefined, so x = 1 is correctly excluded.
Domain: all real numbers where x ≥ 3
On the test: A common pitfall: don’t confuse domain (inputs, x-values) with range (outputs, y-values).
Inside the app, Domain and Range comes with:
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- Math-fact flashcards — Quick drills for addition, multiplication, perfect squares, and square roots.
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