Is there a specific equation involved here? Otherwise, X and Y are unrelated. It's possible for Y to stay the same no matter what you do with X. In this case, when graphing it, you get a line going straight across. Every equation is different, and will cause Y to do different things when you change X.
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If the reflection is over the x value, the x-value does not change.
Using the quadratic formula, you will find for the equation 6x² + 2x + k = 0: x = (-b ±√(b² - 4ac)) / 2a → x = (-2 ± √(2² - 4×6×k)) / (2×6) → x = (-2 ± √(4 - 4×6k)) / (2×6) → x = (-1 ± √(1 - 6k)) / 6 The value of the discriminant (b² - 4ac) affects the value of x: >0 → there are two real values of x; this happens when 1 - 6k > 0 → k < 1/6; =0 → there is one repeated root, ie a single value of x; this happens when k = 1/6 (making x = -1/6); <0 → there are two complex values of x; this happens when k > 1/6.
Yes, it can be the slope of an infinite number of lines. As long as the y-value goes down one for every time the x-value increases by one, the line has a slope of -1.
1/x (not a function though, since it's not defined for x=0). e^(-x) converges close to zero as x increases, would be a good choice.
if value is 1 then its 1, all depends upon value of x