X an asymptote is a line that a curve keeps getting

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Unformatted text preview: r function. y= 1 x y x y=x 0 0 undefined 1 4 1 4 4 1 3 1 3 3 1 2 1 2 2 ( 1 ,4 ) 4 ( 1 ,3) 3 ( 1 ,2) 2 1 1 1 (1,1) 2 2 1 2 3 3 1 3 4 4 1 4 no point 3 y= 1 x -3 (2, 1 ) 2 (3, 1 ) 3 ( 4, 1 ) 4 0 3 -3 The function values for y = 1 are the reciprocals of the function values of y = x . x An asymptote is a line that a curve keeps getting closer to without ever reaching. Function value of the linear function y = x 0 Function value of the linear function's reciprocal function y = 1 x undefined; the reciprocal of 0 does not exist approaches 0 goes toward ∞ or −∞; there will be a vertical asymptote where the linear function value is 0 1 or −1 1 or −1; these are invariant points since the "reciprocal transformation" does not affect these points goes toward ∞ or −∞ approaches 0; if this happens at the far left and right end of the graph there will be horizontal asymptotes at the ends x Unit 6: Day 4 notes - Reciprocal Functions (Part 1) Page 2 of 4 Remember to consider the domain and range of reciprocal functions. GRAPHING y = 1 , THE RECIPROCAL OF A LINEAR FUNCTION ax + b example: Graph of y = 1 by transforming the graph of the linear function. 2x − 3 o Draw the graph of y = 2x − 3 y y = 2x − 3 4 o At the point on the linear graph with y-coordinate 0, the reciprocal graph will not 2 have a point for that x-value; there is probably a vertical asymptote there. y= 1 2x − 3 -2 2 -2 o At the points on the linear graph with y-coordinates approaching 0, the reciprocal graph will have points with y-values going to ∞ -4 or −∞; there is a vertical asymptote at the linear function's x-intercept. o At the points on the linear graph with y-coordinates 1 or −1, the reciprocal graph will have the same points; these are invariant points. o At the points on the linear graph with y-coordinates going to ∞ or −∞; the reciprocal graph will have points approaching the x-axis; the x-axis is a horizontal asymptote for the left and right ends of the reciprocal graph. What is the non-permissible value of ratio...
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