How to reflect over y axis in an equation?

1)  y = -f(x) (This is the reflection about the x-axis of the graph y = f(x).)  That is for every point (x, y) there is a point (x, -y).
2)  y = |f(x)| means that the entire graph will be above the x-axis.  Why?  (The absolute value is always positive, that's why!!)  To graph the absolute value graph, graph the function y = f(x).  Anything above the x-axis, stays above it, anything below the x-axis is reflected above the x-axis and anything on the x-axis, stays on the x-axis.
3)  y = f(-x)  (This is reflection about the y-axis of the graph y = f(x))  For every point on the right of the y-axis, there is a point equidistant to the left of the y-axis.  That is for every point (x, y), there is a point (-x, y).  
4)  Reflections about the line y = x is accomplished by interchanging the x and the y-values.  Thus for y = f(x) the reflection about the line y = x is accomplished by x = f(y).  Thus the reflection about the line y = x for y = x2 is the equation x = y2. 

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