Question

The range of f(x) = |x| is y > 0.

If a < 0 for g(x) = a|x|, what is the range of the function of g?

A. Y < a
B. Y < 0
C. Y > 0

Answer 1

Explanation:

first of all I have to say the range should be " y >= 0" and not just "y > 0", because x can be 0, and then y is 0 too.

but under the the same assumption of the definition above, the correct answer is B, y < 0.

because a×|x| means we multiply a negative value with a positive value. and that result is always a negative value.

so, it cannot be C.

and it cannot be A, because

if |x| < 1 (e.g. 0.5), then a×|x| > a, as e.g. -1 > -2