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MATH 121 Lecture Notes - Lecture 2: Complex Instruction Set Computing

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15 Sep 2016

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$MATH 121 Full Course Notes$

MATH 121 Full Course Notes

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Unit 1: transformation of a functions; exponential and logarithms. Example: transform the graph of y=(cid:2870) into y= 4- (cid:2869)(cid:2870)(cid:4666)+(cid:883)(cid:4667)(cid:2870) y=(cid:2870: y=(cid:2870) y= (cid:4666)+(cid:883)(cid:4667)(cid:2870) The vertical scaling is halved: y= (cid:2869)(cid:2870)(cid:4666)+(cid:883)(cid:4667)(cid:2870) y= - (cid:2869)(cid:2870)(cid:4666)+(cid:883)(cid:4667)(cid:2870) The graph is flipped along the x-axis: y= - (cid:2869)(cid:2870)(cid:4666)+(cid:883)(cid:4667)(cid:2870) y= 4- (cid:2869)(cid:2870)(cid:4666)+(cid:883)(cid:4667)(cid:2870) Vertical shift up 4 spaces. if you ever get confused about the co-ordinates, you can always plug in numbers to the equation. (e. g x=0, y=4- (cid:2869)(cid:2870)(cid:4666)(cid:882)+(cid:883)(cid:4667)(cid:2870) y=4) 4 common types of transformations: horizontal shift, horizontal scaling, vertical shift, vertical scaling: f(x) f(x-a) or f(x+a) Horizontal shift left or right a units f(x) f(ax) Horizontal compression by factor of a if a >1. Horizontal stretch by factor of a if 01.

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