Curriculum
Course: General Mathematics — Second Secondary
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Curriculum

General Mathematics — Second Secondary

Unit 1: Real Functions and Curve Sketching

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Unit 2: Exponents, Logarithms and Applications

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Unit 3: Limits

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Unit 4: Trigonometry

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Text lesson

Monotonicity of Functions

General Mathematics — Second Secondary

Monotonicity of Functions

Definition of monotonicity

Definition of monotonicity

  • The monotonicity of a function describes how it behaves as x moves from left to right through an interval.
  • Let a and b be two numbers in the interval with a < b:
Comparison aspectMain ideaKeywords
Increasingf(a) < f(b) for every a < b in the interval. The graph rises as we move to the righteveryintervalgraphrises
Decreasingf(a) > f(b) for every a < b in the interval. The graph falls as we move to the righteveryintervalgraphfalls
Constantf(a) = f(b) for all a and b in the interval. The graph is horizontalintervalgraphhorizontal
Important
  • always state the interval when you describe monotonicity. A function may be increasing on one interval and decreasing on another
  • so saying “the function is increasing” without an interval is incomplete
alwaysstateintervaldescribe
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