Question

Please help asap. it’s 2 am and idk how to do this

Answer 1

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 $x$, you have two alternative:

• If $x \neq 3$ (i.e., if you've chosen any input that is not 3), the output will be the opposite of the input you've chosen ($y=-x$)
• If $x=3$, the ouput will be -1.

So, let's forget about $x=3$ for a moment. For any input $x$ you choose, the answer is $-x$. 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 $x=3$, 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 $y=-x$, except for one point ($x=3$), where we reassign the value to be -1.