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6-8 Graphing Radical Functions (Half-Graphs) A radical equation defines a radical function. f(x) = √x Translations: Vertical: The graph of the radical function y = √x +k is a translation of y = √x up k units if k is positive and down if k is negative. Ex: y = √x +2 Graph Horizontal Translations: The graph of y = √(x –h) is a translation of y = √x shifted h units to the right if h is positive and h units to the left if h is negative. (You always do the opposite) Ex. y = √(x-2) The graph of y = a√x is a vertical stretch or compression of the graph of y = √x by a factor of a. If a<0, the graph is a reflection across the x axis. Ex. y = -√x Other equations y = x3 and y = 3 √x The translations work the same way. Opposite if in the x direction, the same if in the y direction. You need to memorize these!!! Graph: y= 3 √(x+5) and y = 3 √x +5 Hw pg 418 7-20 25-30 all