Hi my friends!,

I'm sure this is a silly one, but....alas...I do not understand...

a Question like "For which values of x will f(x) < 0?"..is easy, but what does it mean to ask the question like this:

"For which values of x will x(f(x)) < 0" ???.

Please someone..help.....Thank you kindly..

juriemagic Aug 31, 2020

#1**+2 **

Hi Juriemagic,

If x is negative then f(x) would have to be positive (so the product of them is negative)

likewise

If x is positive then f(x) will have to be negative.

Does that help?

Do you have a specific question that is troubling you?

Melody Aug 31, 2020

#2**+1 **

Hi Melody,

Thank you for answering. The question is about a parabola and straight line intercepting on a plane, and all the normal questions one can expect to find, is asked. Then the one I asked about. I was thinking that, to make a drawing of this whole thing just for a 4 point question I do not understand, is way not worth the effort. So, I think I'm going to sit this one out. Anyways, as usual, thank you very much for being out there!!!!..I do appreciate!

juriemagic
Sep 2, 2020

#3**+2 **

Ok how about this.

\(x*f(x)>0 \qquad \\ \text{both factors are positive AND when both factors are negative}\\ \text{x is positive right of the y axis and f(x) is positive above the x axis, so both are positive only in the 1st quadrant.}\\ \text{x is negative left of the y axis and f(x) is negative below the x axis, so both are negative only in the 3rd quadrant.}\\ \)

So the statement will be true whenever the graph is in the 1st or the 3rd quadrant.

Melody
Sep 2, 2020