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Lecture 3

MATA30H3 Lecture Notes - PiecewisePremium

3 pages68 viewsFall 2018

Department
Mathematics
Course Code
MATA30H3
Professor
Xiao Jie
Lecture
3

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MATA30 Lecture 3 Functions 2
Even & Odd Functions
- Even: ƒ(-n) = ƒ(n)
o Replace n with -n, simplify and get back ƒ(n)
o Vertically symmetric across y axis
- Odd: ƒ(-n) = -ƒ(n)
o Replace n with -n, simplify & get back ƒ(n) with –
o Rotated 180˚ about the origin
- Neither: ƒ(-n) ≠ -ƒ(n)
≠ ƒ(n)
Trigonometric Even & Odd Functions
- Sin(x) is ODD Sin(-x) = -sin(x)
- Cos(x) is EVEN cos(-x) = cos(x)
- Tan(x) is ODD tan(-x) = -tan(x)
y = tanx
Piecewise Defined Functions
- Define ƒ(n) in “pieces”
- Differently on different pieces of domain
absolute value |x|
|2| = 2
|-2| = 2 = -(-2)
ƒ(x) = |x| {𝑥 𝑖𝑓 𝑥 0
−𝑥 𝑖𝑓 𝑥 < 0
Increasing/ Decreasing Functions
increasing
o For all x1 < x2, ƒ(n1) < ƒ(n2)
decreasing
o For all x1 < x2, ƒ(n1) > ƒ(n2)
y = sinx y = cosx
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