Well let's start with y = -x^5 and y = - x^5 +1
The graph looks like the one on the right for these two. The red one is y = - x^5 and the blue one is y = - x^5 + 1
See below on the right
You can tell that these two are correct because there is only 1 x axis intercept for each of them. That means there is only 1 real solution which is what you are calling for.
Another one could be something like
y = -(x - 5)(x^2 + 2)(x^2 + 3)
The graph of that is on the left.
