This is an example of a piecewise defined function. It means that the function has not a unique formula to represent it, but it depends on "where" you want to compute it.
So, if you choose any input [tex] x [/tex], you have two alternative:
- If [tex] x \neq 3 [/tex] (i.e., if you've chosen any input that is not 3), the output will be the opposite of the input you've chosen ([tex] y=-x[/tex])
- If [tex] x=3[/tex], the ouput will be -1.
So, let's forget about [tex] x=3 [/tex] for a moment. For any input [tex] x [/tex] you choose, the answer is [tex] -x [/tex]. The graph of this function is the bisector of the second and fourth quadrant.
Now remember that there is our special case: you have to "carve a hole" in our line, at [tex] x=3 [/tex], and assing to this point the value -1, instead of what we would expect, i.e. -3.
So, the graph of this function is the line [tex] y=-x[/tex], except for one point ([tex] x=3 [/tex]), where we reassign the value to be -1.
