What is the reflection of y = f(x)?

Depends on whether you reflect in the x or y-axis.

Reflecting in the y-axis is easy: y = f(x) will become y = - f(x) so, for example y= 3x will become y = -3x on reflecting in the y-axis.

Reflecting in the x-axis,  y = f(x) will become y = f(-x).

This means replace x in the original by -x ( and use brackets)

 y= 4 x -3x²  

will become

y= 4 (-x) -3(-x)²

final answer

 y= -4 x -3x²

If it is a reflection in the y axis then the equation for the reflection of y = f(x)

would be y = f(-x).

If it is a reflection in the x axis then the equation for the reflection of y = f(x)

would be y = -f(x).

If y = 2x + 3

then the reflection in the y axis would be y = 2(-x) + 3 = -2x + 3

and the reflection in the x axis would be y = -(2x + 3) = -2x -3.