K = f x

y = a f (k (x-d) ) + c Where if a is: · a > 1: It is a vertical stretch. · 0 < a < 1 : It is a vertical compression. · a < 0 : There is a reflection in the x- axis. Where if k is: · k > 1: It is a horizontal compression by a factor of (1/k). · 0 < k < 1 : It is a horizontal stretch.

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24.05.2021 K = f x

X x. Lloyd’s Method: k-means Initialize with random clusters. Graph f(x)=k. The function declaration varies according to , but the input function only contains the variable. Assume . Rewrite the function as an equation.

Let's start with an easy transformation. y equals a times f of x plus k. Here's an example y equals negative one half times the absolute value of x plus 3. Now first, you and I ide- identify what parent graph is being transformed and here it's the function f of x equals the absolute value of x.

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X! x " y! 2 2 Easy! y = 1 |X |! x ! X x. Lloyd’s Method: k-means Initialize with random clusters. Graph f(x)=k.

• if 0 < k < 1 (a fraction), the graph is f (x) horizontally stretched by dividing each of its x-coordinates by k. Simplifying g (x) = k * f (x) Multiply g * x gx = k * f (x) Multiply k * f gx = fk * x Multiply fk * x gx = fkx Solving gx = fkx Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Divide each side by 'x'. g = fk Simplifying g = fk You can always share this solution Find an answer to your question if g(x) = k•f(x) what is the value of k Consider the following system of equations.

. , x = x k , where x 1 , x 2 , . . .

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. , x k are roots of Q ( x ). To find the vertical asymptotes of f ( x ) be sure that it is in lowest terms by canceling any common factors, and then find the roots of Q ( x ). Forever F r e a k y F l e x S e a s o n. 137 likes · 2 talking about this.