What does the expression f(x) + or - b represent?

The expression ( f(x) \pm b ) represents a vertical shift of the function ( f(x) ). When you add or subtract a constant ( b ) from ( f(x) ), you are effectively moving the entire graph of the function up or down, depending on whether ( b ) is positive or negative.

For instance, if you have ( f(x) + b ), the graph shifts upward by ( b ) units. Conversely, ( f(x) - b ) results in a downward shift by ( b ) units. This transformation affects the output value of the function for any given input ( x ) without changing the shape or orientation of the graph itself; it simply translates it vertically along the y-axis.

Therefore, the interpretation of ( f(x) \pm b ) as a vertical shift is crucial in understanding function transformations in mathematics.