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Domain & Range: FAST EXAM TRICKS (by function type)
🔥 Domain & Range FAST EXAM TRICKS
Mind-map style revision • Remember fast • Score easy marks
Polynomial
- Domain: (−∞, ∞)
- Linear: Range → (−∞, ∞)
- Quadratic: Vertex gives min / max
- Odd degree: Range → all real
🧠 No √ or fraction? Domain = all real
Rational (Fractions)
- Domain: Denominator ≠ 0
- Solve denominator = 0 → exclude
- Form
a/(x−h)+k→ Range: y ≠ k
Square Root
- Domain: Inside √ ≥ 0
- Range: y ≥ 0 (shift if any)
- √(x−h)+k → y ≥ k
⭐ Golden Rule: Inside √ ≥ 0
Absolute Value
- Domain: (−∞, ∞)
- Vertex gives min / max
- |x|+k → y ≥ k
- −|x|+k → y ≤ k
Exponential
- Domain: (−∞, ∞)
- Range: (0, ∞)
- +k → Range: (k, ∞)
📌 Exponentials never hit 0
Logarithmic
- Domain: Argument > 0
- Range: (−∞, ∞)
- log(x−h) → x > h
Trigonometric
- sin x, cos x → Range: [−1, 1]
- tan x → x ≠ π/2 + kπ
- sec x → (−∞,−1] ∪ [1,∞)
Transformations
- f(x−h) → Domain shifts right
- f(x)+k → Range shifts up
- Horizontal → domain
- Vertical → range
🧠 Ultimate Cheat Sheet
- ❓ Divide by zero? → EXCLUDE
- ❓ √ or log? → inside ≥ 0 / > 0
- ❓ Lowest or highest y-value?