In order to understand this type of transformation, we need to explore how output of the function changes as we add constant value to the output. If we add 1 unit to the function, then each value of function is incremented by 1 unit. It is a straight forward situation. In notation, we would say that the graph of “f(x) + 1” is same as the graph of f(x), which has been moved up by 1 unit. Alternatively, we can also describe this transformation by saying that vertical reference of measurement i.e. x-axis has moved down by 1 unit.

Shifting of graph parallel to y-axis |
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Similarly, if we subtract 1 unit from the function, then each value of function is decremented by 1 unit. In notation, we would say that the graph of “f(x) - 1” is same as the graph of f(x), which has been moved down by 1 unit. Alternatively, we can also describe this transformation by saying that vertical reference of measurement i.e. x-axis has moved up by 1 unit. We conclude :

The plot of y=f(x) + |a|; |a|>0 is the plot of y=f(x) shifted up by unit “a”.

The plot of y=f(x) - |a|; |a|>0 is the plot of y=f(x) shifted down by unit “a”.

We use these facts to draw plot of transformed function f(x±|a|) by shifting plot f(x) by unit “|a|” along y-axis. Each point forming the plot is shifted parallel to x-axis. In the figure below, the plot depicts modulus function y=|x|. It is shifted “1” unit up and the function representing shifted plot is y=|x|+1. Note that corner of plot at x=0 is also shifted by 1 unit along y-axis. Further, the plot is shifted “2” units down and the function representing shifted plot is |x|-2. In this case, corner of plot is shifted by 2 units down along y-axis.

Shifting of graph parallel to y-axis |
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