![]() Putting it all togetherĬonsider the basic graph of the function: y = f(x)Īll of the translations can be expressed in the form: To reflect about the x-axis, multiply f(x) by -1 to get -f(x). To reflect about the y-axis, multiply every x by -1 to get -x. ReflectionsĪ function can be reflected about an axis by multiplying by negative one. With the x, then it is a horizontal scaling, otherwise it is a vertical scaling. Scaling factors are multiplied/divided by the x or f(x) components. The vertical and horizontal scalings can be A horizontal scaling multiplies/divides every x-coordinate by aĬonstant while leaving the y-coordinate unchanged. A vertical scaling multiplies/divides every y-coordinate by a constant while leaving A scale will multiply/divide coordinates and this will change the appearance as well as Scales (Stretch/Compress)Ī scale is a non-rigid translation in that it does alter the shape and size of the graph of theįunction. Then it is a horizontal shift, otherwise it is a vertical shift. Shifts are added/subtracted to the x or f(x) components. Vertical and horizontal shifts can be combined into one expression. A vertical shiftĪdds/subtracts a constant to/from every y-coordinate while leaving the x-coordinate unchanged.Ī horizontal shift adds/subtracts a constant to/from every x-coordinate while leaving the y-coordinate unchanged. All that a shift will do is change the location of the graph. There are three if you count reflections, but reflections are just a special case of theĪ shift is a rigid translation in that it does not change the shape or size of the graph of theįunction. There are two kinds of translations that we can do to a graph of a function. Your text calls the linear function the identity function and the quadratic function the squaring
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