The blue graph is the reflection of the red graph across the x-axis, represented by the equation g(x) = -|x|.
The absolute value function, f(x)=|x|, is a piecewise function that takes any real number as an input and outputs its non-negative value. For example, f(2)=2, f(-2)=2, and f(0)=0.
The graph of the absolute value function is a V-shape that is symmetrical about the y-axis. The function's output is always positive, regardless of the input.
The function g(x)=-|x| is a reflection of the absolute value function across the x-axis. This means that the graph of g(x) is the same as the graph of f(x), but mirrored across the x-axis.
The equation for g(x) is -f(x), which means that the output of g(x) is always the negative of the output of f(x).
In conclusion, the function g(x)=-|x| is the reflection of the absolute value function, f(x)=|x|, across the x-axis. This means that the graph of g(x) is the same as the graph of f(x), but mirrored across the x-axis. The equation for g(x) is -f(x), which means that the output of g(x) is always the negative of the output of f(x).