The range of f(x) = |x| is y ≥ 0. If a < 0 for g(x) = a|x|, what is the range of function g?

range of g(x):  (- ∞, 0)

Step-by-step explanation:

In the absolute value function, the value of a determines whether the graph opens up or down, as well as the wideness or narrowness of the graph. A positive value for a implies that the graph opens up, and is narrower than the parent function, f(x) = |x|.

Given that a < 0 for the function, g(x) = a|x|, then it means that it is a downward-facing parabola, and its maximum point is the vertex. This implies that the y-values will be 0 at most.

Therefore, the range of the function, g(x) is (- ∞, 0).