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First, let's lookat four basic graphs: Y42 y=lxl 32t.51 5lxl+1 2I Horizontal ShiftsWe recognizehoizontal shifts by examining the "inside" what identifies each function type.*Note* The sign "inside" is opposite the direction we move the graph- that is, a minus sign moves thegraph right, and a plus sign moves it left. Also note that any vertical asymptotes will move as well (as inlogarithms, etc)y:(x-1)2 y:lx-l I y:"*-t 1-ln(x-l) v-lY:e' - 20105 Forallthesefunctions,a.,,.n,ffilacewhenthereisaconstantaddedto or subtragted from the function. 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If it is less than 1, it is stretched, and grows more slowly.Y-2x' y:lI/zxl y-ezx 5ln(2x) Combining these techniquesOften, our graphs are combinations of these, with horizontal and vertical translations. As anexample, lets look aty:2(x-t)'- 4. 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