MathAdvanced MathMedium frequency
SAT Math: Domain and Range of Functions
25+ practice questions in Praczo
What you need to know
The concept, explained
- 1
Domain: all valid input values (x). Range: all possible output values (y or f(x)).
- 2
For fractions, exclude x-values that make the denominator zero.
- 3
For square roots (and even roots), the expression under the radical must be ≥ 0.
- 4
For a graph, the domain is read left to right (x-values), the range from bottom to top (y-values).
- 5
The SAT often asks: "Which value is NOT in the domain?" — set the denominator to zero or the radicand to negative and solve.
Common mistakes
- ✗ Confusing domain (inputs) with range (outputs) — domain is x, range is y.
- ✗ For f(x) = 1/(x−3), excluding x = 3 from the range instead of the domain.
Try a sample question
SAT-style practice
What is the domain of f(x) = √(x − 4)?
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