The transformation from the first equation to the second one can be found by finding a a , h h , and k k for each equation. y = a | x − h | + k y = a | x - h | + k Factor a 1 1 out of the absolute value to make the coefficient of x x equal to 1 1 . y = | x | y = | x | Factor a 1 1 out of the absolute value to make the coefficient of x x equal to 1 1 . y = | x | − 4 y = | x | - 4 Find a a , h h , and k k for y = | x | − 4 y = | x | - 4 . a = 1 a = 1 h = 0 h = 0 k = − 4 k = - 4 The horizontal shift depends on the value of h h . When h > 0 h > 0 , the horizontal shift is described as: g ( x ) = f ( x + h ) g ( x ) = f ( x + h ) - The graph is shifted to the left h h units. g ( x ) = f ( x − h ) g ( x ) = f ( x - h ) - The graph is shifted to the right h h units. Horizontal Shift: None
