Question

If you flip the graph of the absolute value parent function f(x) = |x|, over the x-axis, what is the equation of the new function?
A. g(x) = 1/|x|
B. g(x) = -|x|
C. g(x) = |-x|
D. g(x) = |x - 1|

Answer 1

B is indeed the right answer just got it right

Answer 2

The answer is B, $-|x|$.

Here's analyses of the other options:

Option A. You can clearly see that $\frac{1}{|x|}$ is not defined for $x=0$, so the function $\frac{1}{|x|}$ doesn't have the same domain as that of $|x|$, hence can't be the answer.

Option C. By the definition of absolute value, we know that $|-x|=|x|$, this is the same function, hence not the answer.

Option D. This is just $|x|$ shifted one unit to the right, not flipped.