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

Step-by-step 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

the circle one

a) y = -3x +2

b) y = 1/2x -6

these 2 can be combined into one equation.

-3x +2 = .5x -6

8 = 3.5x

x = 8 / 3.5 = 2.2857142857

y = -3 * (8 / 3.5) +2

y = (-24 / 3.5) + 2

y = -4.8571428571

step-by-step explanation: