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All 10 Flashcards — Domain & range
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Question
What is the domain of a function?
Answer
The set of all allowed inputs (x-values).
Question
What is the range of a function?
Answer
The set of all possible outputs (y-values).
Question
How do you read the domain off a graph?
Answer
How far the graph extends left ↔ right (the x-extent).
Question
How do you read the range off a graph?
Answer
How far the graph extends down ↕ up (the y-extent).
Question
What two things restrict a domain?
Answer
No dividing by zero (denominator ≠ 0) and no even root of a negative (under √ ≥ 0). Also a log argument must be > 0.
Question
Domain of 1/(x − 3)?
Answer
x ≠ 3 — the denominator can't be zero.
Question
Domain of √(x − 2)?
Answer
x ≥ 2 — what's under the root must be ≥ 0 (0 is allowed).
Question
Range of f(x) = (x − h)² + k opening upward?
Answer
y ≥ k — the vertex (h, k) is the minimum.
Question
Range of an exponential aˣ (a > 0)?
Answer
y > 0 — always positive, approaching but never reaching 0.
Question
What's the default domain if nothing restricts it?
Answer
All real numbers, x ∈ ℝ.
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Full study notes for Domain & range
Topic 2.2 hub
Functions, domain & range
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