Functions - Inverses of graphs.

Question

The question reads: sketch the graph of y=-3-x along with its inverse.

From calculating the equation of the inverse graph, I come to y=-3-x, using the swap method. I then tried to plot both graphs but they are the exact same, so where does the line of symmetry lie? I can't seem to figure this out.

Any help would be appreciated.

Answer 1

You are right: the function defined by your equation is its own inverse. That is not uncommon, and I have my class deal with several similar functions in homework and a test. Some examples are $y=\frac 1x$ and $y=\sqrt{1-x^2},\ 0\le x\le 1$.

The line of symmetry for all self-inverse functions is the line $y=x$. Your graph also has another line of symmetry, namely itself, but that will not hold for all self-inverse functions. The lines $y=x+c$ for constant $c$ are also lines of symmetry, but again only the one for $c=0$ is important for your question.

Answer 2

Yes the inverse is symmetric to the line $y=x$.

So in this case:

$y=-3-x\therefore x=-3-y\therefore x+3=-y\therefore y=-x-3$

So, $y^{-1}=-x-3$ would be the inverse. And if you plotted $y$ and $y^{-1}$ on a graph, you would see that they are symmetric on the line $y=x$

Answer 3

The line of symmetry is the line $y=x$.

The function $y=-3-x$ is perpendicular to the line and is its own inverse.