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MATH 1113 Review Sheet for the Final Exam
... Section 3.1 Linear Functions Definition: A Linear Function is a function with formula description of the form L(x) = mx + b where m and b are real numbers. The slope of a non-vertical line is the signed vertical displacement corresponding to a one unit increase in the horizontal coordinate. Conn ...
... Section 3.1 Linear Functions Definition: A Linear Function is a function with formula description of the form L(x) = mx + b where m and b are real numbers. The slope of a non-vertical line is the signed vertical displacement corresponding to a one unit increase in the horizontal coordinate. Conn ...
Functions
... Let f1 and f2 be functions from A to R (real numbers).Then •f1+f2 is defined as (f1+f2) (x) = f1(x) + f2(x). •f1f2 is defined as (f1f2)(x) = f1(x)f2(x). And both of these are also from A to R. (Two real valued functions with the same domain can be added and multiplied.) •Example: f1(x) = x2 ; f2 = x ...
... Let f1 and f2 be functions from A to R (real numbers).Then •f1+f2 is defined as (f1+f2) (x) = f1(x) + f2(x). •f1f2 is defined as (f1f2)(x) = f1(x)f2(x). And both of these are also from A to R. (Two real valued functions with the same domain can be added and multiplied.) •Example: f1(x) = x2 ; f2 = x ...
Geometry and Topology, Lecture 4 The fundamental group and
... f∗ : π1 (X , x) → π1 (Y , f (x)) ; [ω] 7→ [f ω] . with the following properties: (i) The identity 1 : X → X induces the identity, 1∗ = 1 : π1 (X , x) → π1 (X , x). (ii) The composite of f : X → Y and g : Y → Z induces the composite, (gf )∗ = g∗ f∗ : π1 (X , x) → π1 (Z , gf (x)). (iii) If f , g : X → ...
... f∗ : π1 (X , x) → π1 (Y , f (x)) ; [ω] 7→ [f ω] . with the following properties: (i) The identity 1 : X → X induces the identity, 1∗ = 1 : π1 (X , x) → π1 (X , x). (ii) The composite of f : X → Y and g : Y → Z induces the composite, (gf )∗ = g∗ f∗ : π1 (X , x) → π1 (Z , gf (x)). (iii) If f , g : X → ...
1 Metric spaces
... 1.5 De…nition (i) : The map f : X ! Y between metric spaces X; Y is continuous at a 2 X if 8 neighbourhoods N of f (a) 9 a neighbourhood M of a such that f (M ) N . (ii) f is said to be continuous on X or continuous if f is continuous at each point of X. (i) f is a homeomorphism if it is one-to-one, ...
... 1.5 De…nition (i) : The map f : X ! Y between metric spaces X; Y is continuous at a 2 X if 8 neighbourhoods N of f (a) 9 a neighbourhood M of a such that f (M ) N . (ii) f is said to be continuous on X or continuous if f is continuous at each point of X. (i) f is a homeomorphism if it is one-to-one, ...