Question

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 1

The absolute value parent function is symmetric with respect to the y-axis.

The graphs of f(x) = 2|–x| and f(x) = 2|x| are identical because the absolute value of negative x is a reflection across the y-axis.

If you substitute the three given points into both functions, they produce true statements.

Explanation:

Answer 2

In mathematics, the absolute value or modulus. | x. | of a real number x is the non-negative value of x without regard to its sign. So both shawn and brielle are correct since both function will have the same answer, because it will just cancel out the sign.