DSE often combines ( y = |f(x)| ) or ( y = f(|x|) ) with other transformations.
Every transformation can be categorized into one of four movements. To succeed, you must distinguish between changes (affecting the output ) and Horizontal changes (affecting the input A. Translation (Shifting) Vertical Shift: +kpositive k moves the graph up ; −knegative k moves it down . Horizontal Shift: Counter-intuitive rule: moves the graph right , while moves it left . B. Reflection (Flipping) Reflection in x-axis: The graph flips upside down (all -coordinates change sign). Reflection in y-axis: The graph flips horizontally (left becomes right). C. Scaling (Enlarging/Compressing) Vertical Stretch/Compression: , the graph stretches vertically. If , it compresses. Horizontal Stretch/Compression: Counter-intuitive rule: If , the graph compresses horizontally by a factor of , it stretches . 2. Common DSE Pitfalls to Avoid The "Opposite" Rule for : Students often forget that operations inside the bracket transformation of graph dse exercise
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Given ( f(x) = |x| ), write the equation for: DSE often combines ( y = |f(x)| )
: Horizontal compression → Horizontal translation → Vertical stretch → Reflection → Vertical translation. Reflection (Flipping) Reflection in x-axis: The graph flips
: A translation vector ( -2, 0 ) means a horizontal shift 2 units to the left. The new equation is therefore y = f(x + 2) .