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Domain & Range: FAST EXAM TRICKS (by function type)
π₯ Domain & Range FAST EXAM TRICKS
Mind-map style revision β’ Remember fast β’ Score easy marks
Polynomial
- Domain: (ββ, β)
- Linear: Range β (ββ, β)
- Quadratic: Vertex gives min / max
- Odd degree: Range β all real
π§ No β or fraction? Domain = all real
Rational (Fractions)
- Domain: Denominator β 0
- Solve denominator = 0 β exclude
- Form
a/(xβh)+kβ Range: y β k
Square Root
- Domain: Inside β β₯ 0
- Range: y β₯ 0 (shift if any)
- β(xβh)+k β y β₯ k
β Golden Rule: Inside β β₯ 0
Absolute Value
- Domain: (ββ, β)
- Vertex gives min / max
- |x|+k β y β₯ k
- β|x|+k β y β€ k
Exponential
- Domain: (ββ, β)
- Range: (0, β)
- +k β Range: (k, β)
π Exponentials never hit 0
Logarithmic
- Domain: Argument > 0
- Range: (ββ, β)
- log(xβh) β x > h
Trigonometric
- sin x, cos x β Range: [β1, 1]
- tan x β x β Ο/2 + kΟ
- sec x β (ββ,β1] βͺ [1,β)
Transformations
- f(xβh) β Domain shifts right
- f(x)+k β Range shifts up
- Horizontal β domain
- Vertical β range
π§ Ultimate Cheat Sheet
- β Divide by zero? β EXCLUDE
- β β or log? β inside β₯ 0 / > 0
- β Lowest or highest y-value?