Question

Which absolute value function, when graphed, represents the parent function, f(x) = |x|, reflected over the x-axis?

f(x) = –|x|

f(x) = |–x|

f(x) = |x| + 1

f(x) = |x – 1|

Answer 1

I believe reflection is just saying the opposite of current function so if the function is x then the opposite of that would be -x

in this case the function is |x| so the opposite would be -|x|

Answer 2

f(x) = - |x| is the correct answer.

Explanation:

We are given the function f(x) = |x| and are required to reflect this function across x- axis.

Now, reflection of a graph across x- axis means we are taking mirror image of the function across x- axis.

Moreover, mirror image does affect the behaviour of the function just the values of the function are negated i.e. f(x) becomes -f(x).

Hence, the reflection of f(x) = |x| is f(x) = -|x|.

It can also be seen in the figure below.