I don't know what mini(x) is, but flipping a graph over the y-axis means that every point that was (x,y) becomes (-x,y) after the reflection. Like, if (8,3) is a point in the original function, (-8,3) is a point in the reflected function. So the output values are the same, but for the negative versions of the input values.
I hope this helps!
Have fun mathing!
Liz Z.