Thread: Inequalities/writing set in interval notation

So far I've gathered that the critical numbers are x = 1 and x= -2. I graphed them on the number line. I plugged in test values for each of them.

When I do that, for every test value I've plugged in they've been .

Now I don't know what that means. Does that mean that since every test proved to be a positive, it'll be the whole thing?

The test intervals were .

I'm also confused on this problem:



I already know what it turns into.



That wasn't the hard part. The hard part is figuring out the critical numbers for this.




1 -x+x -x^2


and

is supposed to be a critical number, but I don't know how you get that.

Yup looks good to me.

Thanks, I updated it with a second problem. I got 2 of the critical numbers. I dunno how you get zero cause in the back of the book it said 0 was a critical number. Only one I'm missing.

Critical numbers are where the either the numerator or the denominator equal 0. So x=0 for this problem sets the denominator to 0 and could possibly change the direction.

Example: f(x)=1/x

At x=0 there is obviously an asymptote but the direction of the graph is opposite from each side.