2.6 – Vertical and Horizontal Translations

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Presentation transcript:

2.6 – Vertical and Horizontal Translations

Translating Functions A translation is an operation that shifts a graph horizontally, vertically, or both. The results are a graph of the same size and shape, just in a different position

Y = |x + 2| – 3 Parent Function: the simplest function with the given characteristics (-2 , -3)

Y = |x + 5| + 8 (-5 , 8)

Y = |x – 8| – 6 (8 , -6)

Y = |x – 7| + 4 (7 , 4)

Y = |x – 4| – 5 (4 , -5)

Y = |2x – 8| + 2 (4 , 2)

Y = |3x + 6| – 3 (-2 , -3)

Is there a formula for graphing absolute value equations??? Y = |x + 2| – 3 Y = |x + 5| + 8 Y = |x – 8| – 6 Y = |x – 7| + 4 Y = |x – 4| – 5 Y = |2x – 8| + 2 Y = |3x + 6| – 3 Y = |mx + b| + c (-2 , -3) (-5 , 8) (8 , -6) (7 , 4) (4 , -5) (4 , 2) (- b/m , c)

What is the pattern? Y = |mx + b| + c What does the m (slope) do to the graph? (- b/m , c)