Functions y=x and y=x-3 are related in a way that each output for y=x–3 is 3 units more than the corresponding output for y=x.
Their graphs are related in a way that the graph of y=x–3 is the graph of y=x translated down 3 units
A function will defines one variable in terms of the other. Functions y=x means that y will vary directly to whatever value x takes.
When the graph of function y=x is drawn, then it is a straight line through the origin.
Now, functions y=x and y=x-3 are closely related. The graphs of the two are almost the same, the only difference is that every point on function y=x has been lowered by 3 to be function y=x-3.
Hence, the output for y=x-3 is 3 units more than the output of y=x, and the graph of function y=x is translated down by 3 units to get function y=x-3
The graphs for functions y=x and y=x-3 are shown below:
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