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The function f(x) is mirror transformed or reflected about the y-axis by representing it as f(-x). The point (x, y) has not been changed to (x, -y). The point (x, y) with reference to the function f(x) is now transformed to (x, -y).Īn an example the function f(x) = 3x +2 is transformed to is flipped across the x-axis and is represented as -f(x) = -(3x + 2). The function f(x) is flipped transformed about the x-axis by writing it as -f(x) and it is a mirror reflection of the function f(x) about the x-axis. And a point (x, y) with reference to the earlier function is now represented as (x - 2, y). Let us consider a function f(x) = 2x + 3, to be shifted horizontally about the x-axis, by 2 units to the left and the new function would be f(x + 2) = 2(x + 2) + 3. moves to the left if x is replaced by x + a. In this case, a point (x, y) of f(x) becomes (x - a, y) of f(x + a).In this case, a point (x, y) of f(x) becomes (x + a, y) of f(x - a). moves to the right if x is replaced by x - a.
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In this transformation, the graph of a function moves to the left side or right side. In this case, the point (x, y) with reference to f(x, y), has been changed to (x, y - a), for the new transformed function f(x) - a.Īs an example the function f(x) = x 3+ 2x 2 has been vertically transformed by 4 units for f(x) = x 3 + 2x 2 + 4., and a point (x, y) with reference to the earlier function is not represented as (x, y + 4). If the function f(x) has been vertically shifted downwards by 'a' units then the result is the function f(x) - a.In this case, the point (x, y) with reference to the function f(x) changes to (x, y + a) for the new function f(x) + a. If the function f(x) has been vertical shifted upwards by 'a' units then the result is the function f(x) + a.In the vertical transformation, the graph moves either up or down. The function transformation rules can be shown as change in the graph of the function in the coordinate axis. The change in the domain or the range of the function, can be understood by the change in the x-values and the y-values. The domain of the function - the x value can be represented along the x-axis, and the range of the function - the y value can be represented along the y-axis. The rules of transformation for functions can be represented graphically across the coordinate axis. Graphical Representation of Rules of Transformation If c >1 then it is stretched vertically, and if 0 1 then it is compressed horizontally, and if 0 < c < 1 then it is stretched horizontally. Stretched/Compressed Vertical Transformation: The function f(x) is stretched/compressed vertically if a constant 'c' transforms it to cf(x).Mirror Transformation About the Y-axis: The function f(x) is changed to -f(x) to obtain a mirror transformation about the y-axis.Flipped Transformation about the X-axis: The function f(x) is flipped about the x-axis by writing it as f(-x).And it is transformed towards the right on replacing f(x) with f(x - a). Horizontal Transformation: The function f(x) is shifted towards the left for the new function f(x + a).And the function f(x) is shifted vertically doward Vertical Transformation : The function f(x) is shifted up by 'a' units upwards for the function f(x) + a.The six important rules of transformation are as follows. Rules of transformation represent these changes in the x or y values of the function. Similarly the change of the range of the function is possible by replacing f(x) with -f(x), f(x) + 3, f(x) - 2, f(x)/4. The transformation of a function to change the domain of the function is to replace the x value with a new value of x such as x + a, 5x, x - 3, x/2. For a function y = f(x), the domain is the x value and the range is the f(x) or the y value of the function.
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Function transformation rules help in transforming the function based on the change of either the domain or the range of the function.