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I'm trying to answer a question that says, State where $f(x)<0$ using any correct notation and I do not know what it is asking for. The question provides me a graph going from quadrant 2 to 4, and based on that graph I'm supposed to "State where $f(x)<0$ using any correct notation".

Note, this is a homework problem but I am not asking you to answer the question. Just help me to understand what is being asked.

Hirshy
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Michael
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    At a guess: "For which $x$ is $f(x)<0$". – lulu Aug 01 '15 at 12:22
  • @lulu so does that mean where the x-intercept is less than 0? – Michael Aug 01 '15 at 12:23
  • Your title says "f(x) < 0", but your question says "f(x) < )". Which one is it? The former makes sense, the latter looks like a typo to me. – rywit Aug 01 '15 at 12:25
  • the former is correct, latter is a typo. – Michael Aug 01 '15 at 12:25
  • No...the x-intercept is the solution to $f(x)=0$. I'm guessing they want all the $x$ for which $f(x)$ is negative. Should be some range of $x$, not a single value. Just guessing of course. – lulu Aug 01 '15 at 12:25
  • @lulu so that means all the x where y is negative? f(x) is y i.e. the range? – Michael Aug 01 '15 at 12:27
  • That's my reading yes. That would be a fairly standard sort of question...easy to solve if you have the graph or, possibly, if you have a nice form for the function. Good luck! – lulu Aug 01 '15 at 12:29

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enter image description here

This is an example picture, I think/hope that it is in some way similar to yours. Now, $f(x)<0$ means, that the graph lies below the $x$-axis. In this case we have $f(x)<0$ when $x$ lies between $-1$ and $-0.5$ or when $x$ lies between $0$ and $1$. This can be expressed in a few different ways, hence there is more than only one correct notation.

  • $(-1,-0.5)\cup (0,1)$ uses the intervall notation
  • $]-1,-0.5[\cup ]0,1[$ again uses the intervall notation but with different brackets to exclude the end points
  • $\{x\in\mathbb R~|~-1<x<-0.5~\vee 0<x<1\}$

There are more possible ways to write this down, you just have to choose your favourite.

Hirshy
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