FUNCTION TRANSLATIONS ADV151 TRANSLATION: a slide to a new horizontal or vertical position (or both) on a graph. f(x) = x f(x) = (x – h) Parent function.

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FUNCTION TRANSLATIONS ADV151 TRANSLATION: a slide to a new horizontal or vertical position (or both) on a graph. f(x) = x f(x) = (x – h) Parent function at origin. Function translated horizontally. (x + h) is h units left and (x – h) is h units right because horizontal changes are inversed. f(x) = (x) + k Function translated vertically. (x) + k is k units up. (x) – k is k units down. f(x) = (x + h) f(x) = (x) – k

FUNCTION TRANSLATIONS ADV151 g(x) = (x – 2) + 6 The 2 is a horizontal shift right and the 6 is a vertical shift up. Basically you add 2 to every x-coordinate and add 6 to every y-coordinate. g(x) = (x + 4) The +4 is grouped with the x so it’s a horizontal translation. Basically you subtract 4 from every x-coordinate. g(x) = (x) + 3 The +3 is NOT grouped with the x so it’s a vertical translation. Basically you add 3 to every y-coordinate.

FUNCTION TRANSLATIONS ADV151 g(x) =  x – 2  + 7 h(x) = – 5 1 x – 3 f(x) = (x + 5) 2 – 4 g(x) = Describe the translation of each function. Answers on next slide.

FUNCTION TRANSLATIONS ADV151 g(x) =  x – 2  + 7 h(x) = – 5 1 x – 3 f(x) = (x + 5) 2 – 4 g(x) = Describe the translation of each function.ANSWERS! 2 units right 7 units up 5 units left 4 units down 1 units right 4 units up 3 units right 5 units down