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 Introduction to Functions Transformations There are many different transformations, and graphing transformations is different depending on what type it is. Here is a summary of simple transformations: Transformation from f(x) to f(kx) where k is i) a positive integer greater than 1, double or treble, i.e., the value of x is replaced by 2x or 3x. The function is stretched by a scale factor of or , i.e., it is squashed. ii) a positive fraction or , the value of x is replaced by or , that is the graph is stretched by a factor of 2 or 3. Transformation f(x) to f(x)+k, where k is i) a positive integer, thus shifting the graph upwards vertically by k units. ii) a negative integer, thus shifting the graph downwards vertically by k units. Transformation of y=f(x) to y=f(x+k). The graph is translated by k units parallel to the y-axis. When k is a positive integer, the graph is translated to the left k units parallel to the y-axis and when k is a negative integer, the graph is translated to the right k units. Transformation of y=f(x) to y=-f(x). The graph is reflected in the x-axis. Transformation of y=f(x) to y=f(-x). The graph is reflected in the y-axis. Transformation of y=f(x) to . In this case we take the reciprocal.