How am I supposed to interpret the negative and positive intervals in this graph?

Question

The Graph:

I'm tripped up over paragraph two. I don't think it's right. I think the graph is negative at $-10 < x < -9$ and $-2 < x < 4$ and positive at $-9 < x < -2$ and $4 < x < 10$.

Answer 1

Not only you're absolutely right, but it is a pretty poor phrasing altogether to say that a graph is negative. A number can be negative, not a graph. It is important to understand that maths is made of objects of different nature (that can be related in a number of ways) and to use precise and appropriate terminology so as not to mix up these objects.

I wouldn't recommend this book to any of my classes, at any level.

Answer 2

Yes it is correct, we can say that

• $f$ is negative for $-10<x<-9$ and $-2<x<4$
• $f$ is positive for $-9<x<-2$ and $4<x<10$

since we don't have information for values $x<-10$ and $x>10$.