The graph of an absolute value function contains the points (1, 2), (0, 0), and (–1, 2). Shawn thinks the function this graph represents is f(x) = 2|–x|. Brielle thinks the function this graph represents is f(x) = 2|x|. Determine who is correct and explain why.

Answer:

Both Shawn and Brielle are correct. The functions f(x) = 2|-x| and f(x) = 2|x| are equivalent because the absolute value of a number is the same as the absolute value of its opposite (|-x| = |x|). When you substitute the points (1, 2), (0, 0), and (–1, 2) into both equations, they yield true statements. Graphically, f(x) = 2|-x| represents a reflection of f(x) = 2|x| across the y-axis, and since the absolute value parent function is already symmetric with respect to the y-axis, the graphs are identical.