Questions: The graph of y=x is the solid black graph below. Which function represents the dotted graph?

Solution Steps

The solid black graph represents \(y = |x|\). This is the absolute value function, and its vertex is at the origin (0,0).

The dotted graph is also a V-shape, similar to the absolute value function. It also has its vertex at the origin (0,0). However, it is reflected across the x-axis, meaning the output values (y-values) are negated.

Since the dotted graph is a reflection of \(y = |x|\) across the x-axis, its equation is \(y = -|x|\).

Final Answer