Answer:
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).
