# Thread: The intervals where the function is positive and negative.

1. ## The intervals where the function is positive and negative.

Having trouble with finding the "the intervals where the function is positive and negative", I know what the zeros are but I'm not sure how to word it correctly. Heres a picture of the question and my answers to them.

Example in my notes.

I feel like I'm either messing up my > or < signs or my zeros are wrong.

2. ## Re: The intervals where the function is positive and negative.

Let's start with a). If $x<-2$, then we have $f(x)$ is the product of 4 negative numbers: $-4, (x-3), (x+2), (2x-1)$, so it is positive.
If $-2<x<\dfrac{1}{2}$, we have $f(x)$ is the product of three negative numbers: $-4, (x-3), (2x-1)$ and one positive number $(x+2)$, so it is negative.
If $\dfrac{1}{2} < x < 3$, we have $f(x)$ is the product of two negative numbers: $-4, (x-3)$ and two positive numbers: $(x+2), (2x-1)$, so it is positive.
If $3 < x$, we have $f(x)$ is the product of one negative number: $-4$ and there positive numbers: $(x+2), (2x-1), (x-3)$.

For part (b), you have the zeros wrong. -2 is not a zero, but 0 is.

3. ## Re: The intervals where the function is positive and negative.

What does "zero of a function" mean?