This is a picture of my math quiz in which I got a question wrong.
I feel I should not lose points as the question is to ambiguous. I assumed that if one point lied above x-axis then that would constitute as the graph lying above the x-axis. My teacher interpreted it as all points must lie above. Is she right?
Note $x<-1$ refers to all of the points less than $-1$ so no, one point is not enough.
Yes your teacher is correct under the usual conventions.