Three key graph transformations involving modulus: (1) y = |f(x)|: take graph of f(x), reflect parts below x-axis upward. The graph never goes below x-axis. (2) y = f(|x|): keep the right half (x>=0) of f's graph, reflect it symmetrically to the left. Graph is symmetric about y-axis. (3) |y| = f(x): keep parts of f's graph where f(x)>=0, reflect them below x-axis. Graph is symmetric about x-axis. JEE may ask: "how many solutions does |sin x| = x/10 have?" — answer by counting intersections of y=|sin x| and y=x/10 graphically.