So the "a" and "b" there areĪctually multipliers (even though they appear on the bottom). Thought of how far to go in the x-direction (an x-scaling) and the "b" couldįar to go in the "y" direction (a y-scaling). Where a was the x-intercept and b was the y-intercept of the line. Trigonometry (Math 117) and Calculus (Math 121, 122, 221, or 190).Įarlier in the text (section 1.2, problems 61-64), there were a series of problems which wrote the Understanding the concepts here are fundamental to understanding polynomial and rationalįunctions (ch 3) and especially conic sections (ch 8). 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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