- Distance in the Plane
Recall that Pythagorean Formula is: Z^2 = X^2 + Y^2
Distance Formula: Dist(A,C)= Sqrt((C-A)^2 + (D-B)^2)
- Nearest neighbours How far away is one point from another vs another point
Lines in the Plane, Part I Y - Y1 = M(X - X1) = point slope
Y = Mx + b -> Slope, Intercept, Part 2
Slope M, is (Y1 - Y) / (X1 - X)
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Clustering
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Point slope formula of line
If a line l has slope M and if (X, Y) is any point on the line then l has equation Y1 - Y = M(X1 - X)
If a line l has slope M and l hits the Y axis at the point (0, b) then y = mx + b is an equation for the line. M is the slope and b is the y intercept
Functions from set to set
f:A->B is a rule/ formula/ machine which transforms each A element A into f(a) element B
Examples:
A = {1, 2, 10} B = {Apple, DE, Monkey}
f: A -> B f(1) = Apple
Supervised Learning Profit: Years -> IR
f:A->B
Graphing of Functions
Increasing and Decreasing Functions
Composing and Inverse
Composing 2 functions
- Basic idea
- A warning
Inverse Functions
- Basic Idea
- A neat Picture
- A warning
f(x) = x^2 g(x) = x + 5
If graph of f fails the horizonal line test, F has no inverse