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There are four common types of transformations - translation, rotation, reflection, and dilation.
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. 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.
Apply the transformations in this order: Start with parentheses (look for possible horizontal shift) (This could be a vertical shift if the power of x is not 1.) Deal with multiplication (stretch or compression) Deal with negation (reflection) Deal with addition/subtraction (vertical shift)
Given a function and both a vertical and a horizontal shift, sketch the graph. Identify the vertical and horizontal shifts from the formula. The vertical shift results from a constant added to the output. The horizontal shift results from a constant added to the input. Apply the shifts to the graph in either order.
Types of Transformations TransformationFunction Rotation Rotates or turns the pre-image around an axis Reflection Flips the pre-image and produces the mirror-image Translation Slides or moves the pre-image Dilation Stretches or shrinks the pre-image

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To find the function transformations we have to identify whether it is a translation, dilation, or reflection or sometimes it is a mixture of some/all the transformations. For a function y = f(x), if a number is being added or subtracted inside the bracket then it is a horizontal translation.

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